UNIT: PYTHAGOREAN THEOREM AND IRRATIONAL NUMBERS

Ariel completed the work below to show that a triangle with side lengths of 9, 15, and 12 does not form a right triangle. Is Ariel's answer correct? No, Ariel should have added 122 and 152 and compared that to 92. No, Ariel should have subtracted 122 from 92 and compared that to152. No, Ariel should have added 92 and 122 and compared that to 152. Yes, Ariel's work is correct.

No, Ariel should have added 92 and 122 and compared that to 152.

What is the length of the hypotenuse of the triangle? 26 ft 34 ft 68 ft 74 ft

Not 34ft

Which point best approximates ? A B C D

c

Which inequalities are true? Select the four correct answers.

1,2,3,6

A moving van ramp is 72 inches in length. The top of the ramp can be adjusted to any height up to 20 inches. The ramp is set so that the distance across the ground from the bottom of the ramp to the ground underneath the top of the ramp is 70 inches. What is the height of the ramp above the ground? Round the answer to the nearest tenth of an inch. 2.0 inches 10.0 inches 16.9 inches 69.2 inches

16.9

Denesh is creating a triangular flower bed using three pieces of wood. The two shorter pieces of wood have lengths of 7 feet and 24 feet. How long, in feet, should the third piece of wood be for Denesh to create a right triangle?

25

Which is a perfect square? 20 21 24 25

25

Which fraction has a repeating decimal as its decimal expansion?

3/11

In a right triangle, the hypotenuse has endpoints XY, shown on the graph. If Z represents the third vertex in the triangle and is located in the second quadrant with integer coordinates, what is the length of YZ? 3 4 5 6

5

Which is the best estimate of to the nearest tenth? 6.8 6.9 7.0 7.1

6.9

Which is converted to a simplified fraction?

6/11

Sam said the square root of a rational number must be a rational number. Jenna disagreed. She said that it is possible that the square root of a rational number can be irrational. Who is correct and why? Jenna is correct because all square roots are irrational numbers. Sam is correct because all square roots of rational numbers are rational. An example is . Jenna is correct because not all square roots are rational. An example is Sam is correct because the properties of square roots state that the square root of a rational number is a rational number.

Jenna is correct because not all square roots are rational. An example is

Jillian said is irrational because it is a square root. Why is she incorrect? Jillian is incorrect because the square root of . Jillian is incorrect because a square root is always rational. Jillian is incorrect because square roots of perfect squares are rational. Jillian is incorrect because the decimal expansion of is a repeating decimal.

Jillian is incorrect because square roots of perfect squares are rational.

A wire that is 22 feet long connects the top of a pole to the ground. The wire is attached to the ground at a point that is 10 feet from the base of the pole. What is the height of the pole? Round to the nearest hundredth. 12.00 feet 19.60 feet 24.17 feet 38.40 feet

NOT 38.40 ft

What is the length of segment GH? units 8 units units 12 units

NOT 8units

Sanjay, Colby, and Arpitha are training to run a marathon. On Saturday, Sanjay ran miles, Colby ran 13 miles, and Arpitha ran the shortest route from the library to her house, as shown in the diagram. Which list shows the names in order from the person who ran the shortest distance to the one who ran the greatest distance? Colby, Sanjay, Arpitha Sanjay, Arpitha, Colby Sanjay, Colby, Arpitha Arpitha, Sanjay, Colby

NOT Sanjay, Colby, Arpitha

What is the length of a diagonal of a cube with a side length of 3 cm? cm cm cm cm

NOT Square root of 18cm

Which irrational number can be added to to get a sum that is rational?

NOT a

Tyree is determining the distance of a segment whose endpoints are A(-4, -2) and B(-7, -7).Step 1: Step 2: Step 3: Step 4: Step 5: Therefore, d = 2.Which best describes the accuracy of Tyree's solution? Tyree's solution is accurate. Tyree's solution is inaccurate. In step 1, he substituted incorrectly. Tyree's solution is inaccurate. In step 2, he simplified incorrectly. Tyree's solution is inaccurate. In step 3, he added incorrectly.

Tyree's solution is inaccurate. In step 1, he substituted incorrectly.

Which is the correct classification and decimal expansion of ? irrational number, irrational number, rational number, rational number,

c

What is the length of the unknown leg in the right triangle? mi mi mi mi

32 square root

Which is a perfect square? 5 8 36 44

36

Which is a diagonal through the interior of the cube?

AH

Which expression will equal a rational product even though it is multiplying an irrational number times another irrational number?

square root of 11 Times Square root of 11

The values and are plotted on the number line.What is the approximate difference in tenths between and ? 0.2 0.4 1.5 1.7

0.4

The values and are plotted on the number line. What is the approximate difference in tenths between the two values? 0.5 0.9 1.1 2.4

0.9

Fahim is 6 feet tall. At noon, he stands with the sun behind him casting a shadow. The distance from the top of Fahim's head to the furthest tip of the shadow is 13 feet. [Not drawn to scale]What is the length of Fahim's shadow? Round to the nearest tenth of a foot. 7.0 feet 8.5 feet 11.5 feet 14.3 feet

11.5 ft

A diagonal of a cube measures 15 cm and the length of an edge of the cube is cm. What is the length of the diagonal of a face of the cube? Round to the nearest tenth. 7.1 cm 12.2 cm 13 cm 15 cm

12.2

Which is a perfect square? 121 140 168 195

121

How long a ladder must you have to reach the top of a 15-foot wall if the bottom of the ladder is placed 4 feet from the base of the wall? Round to the nearest tenth of a foot. 14.5 ft 15.5 ft 17.0 ft 19.0 ft

15.5 ft

A diagonal of a cube measures cm. The diagonal of a face measures cm. In centimeters, what is the length of an edge of the cube? Round the answer to the nearest tenth. centimeters

15.8

Which equation can be used to find x, the length of the hypotenuse of the right triangle?

18^2 +24^2=x^2

What is the length of the unknown leg in the right triangle? 8 cm 16 cm 20 cm 40 cm

20cm

What is the length of the missing leg in this right triangle? 18 mm 24 mm 26 mm 32 mm

24mm

Reynaldo rode his bike 2 miles north and 3 miles east. Which equation should he use to find the distance, d, that takes him directly back home?

2^2+3^2=d^2

Which is the length of the hypotenuse of the triangle? ft ft 33 ft 37 ft

37ft

Which statement explains why 49 is a perfect square? 49 can be multiplied by 49. 49 is equal to 7 plus 7. 49 is between 36 and 64. 49 is equal to 7 times 7.

49 is equal to 7 times 7.

Which simplified fraction represents 0.45 repeating

5/11

Which simplified fraction represents ?

5/11

What is the length of the diagonal of a cube with a side length of 4 inches? Round to the nearest tenth. 5.7 inches 6.9 inches 8.4 inches 17.7 inches Submitted

6.9

Which is a perfect square? 6^1 6^2 6^3 6^5

6^2

Which equation could be used to find the length of the hypotenuse?

6^2+11^2=c^2

Which two numbers does lie between on a number line? 7.0 and 7.1 7.1 and 7.2 7.2 and 7.3 7.3 and 7.4

7.2 and 7.3

Which two numbers does lie between on a number line? 7.7 and 7.8 7.8 and 7.9 7.9 and 8.0 8.0 and 8.1

7.8 and 7.9

What is the sum and classification of ? 9.78083151..., irrational 9.78083151..., rational 13.38083151..., irrational 13.38083151..., rational

9.78083151..., irrational

Segment is 7 inches and is inches. What is the length of ? Round to the nearest tenth. 7.0 inches 9.9 inches 12.1 inches 14.0 inches

9.9 inches

Which is a diagonal through the interior of the cube?

BG

Kendra is determining the distance between the points (6, 8) and (2, -3). Her work is shown below. Step 1: Step 2: Step 3: Step 4: Which best describes the accuracy of Kendra's solution? Her solution is correct. Her solution is incorrect. She subtracted before squaring. Her solution is incorrect. She made an error when substituting the x-values into the equation. Her solution is incorrect. She made an error when substituting the y-values into the equation.

Her solution is incorrect. She made an error when substituting the y-values into the equation.

Four students provide the following approximations for .Anyah states that is between 0.44 and 0.45 because .Matthew states that is between 0 and 1 because .Rhoda states that is between 0.9 and 1.0 because .Ming states that is between 0.93 and 0.95 because .Which solution(s) are correct? Anyah's only Ming's only Anyah's, Matthew's, and Rhoda's Matthew's, Rhoda's, and Ming's

Matthew's, Rhoda's, and Ming's

Which triangle's unknown side length measures 7 units? Submitted

NOT c

The sum of a rational number and an irrational number equals: a terminating decimal. a rational number. a fraction. an irrational number.

an irrational number.

Which simplified fraction is equal to 0.17 repeating ?

b

A builder set up a wooden frame in which to pour concrete for a foundation to a house. The length of the wooden frame is 24 feet. The width is 32 feet. The diagonal is 40 feet. Which best describes the foundation? The foundation cannot be a rectangle: . The foundation cannot be a rectangle: . The foundation cannot be a rectangle: . The foundation may be a rectangle: .

d

Each point on the edge of a circle is equidistant from the center of the circle. The center of a circle is located at (6, 3). Which point on the y-axis could be on the edge of the circle if the distance from the center of the circle to the edge is 10 units? (0, -1) (0, 1) (0, 5) (0, -5)

d

What is the distance between (-6, 2) and (8, 10) on a coordinate grid?

d

Which is the correct classification of ? irrational number, non-repeating decimal irrational number, terminating decimal rational number, terminating decimal rational number, non-repeating decimal

irrational number, non-repeating decimal

The areas of the squares formed by the side lengths of the triangles are given for each triangle below. Which triangles are right triangles? Select the three correct answers. (Figures are not drawn to scale.) Submitted

not 1 4 6 together

Which expressions represent rational numbers? Check all that apply.

not 1,5,6

A diagonal of a cube measures 15 cm and the length of an edge of the cube is cm. What is the length of the diagonal of a face of the cube? Round to the nearest tenth. 7.1 cm 12.2 cm 13 cm 15 cm

not 13

Which expressions represent rational numbers? Check all that apply.

not 2 and 4

Which number is farthest from 2 on the number line?

not 2.9

Which inequalities are true? Select the four correct answers.

not A,b,c, and f together

Which is a right triangle formed using a diagonal through the interior of the cube? triangle ABE triangle ABD triangle ADH triangle ACE Submitted

triangle ABE

Which numbers are perfect squares? Check all that apply. 1 2 16 18 32 44 94 100

1 16 100

Which simplified fraction is equal to ?

8/15

The point is plotted on the number line. What whole number best approximates the value of x? 100 102 103 104

104

Which two numbers does lie between on a number line? 11.0 and 11.1 11.2 and 11.3 11.3 and 11.4 11.4 and 11.5

11.3 and 11.4

A ladder that is 14 feet long is placed against a building. The bottom of the ladder is 6 feet from the base of the building. In feet, how high up the side of the building is the top of the ladder? Round to the nearest tenth of a foot. Submitted

12.6

Which set of side lengths forms a right triangle? 2, 3, 13 4, 6, 10 9, 12, 18 15, 36, 39

15, 36, 39

What is the distance between (-13, 9) and (11, 2) on a coordinate grid?

25

Which equation can be used to find the unknown length, b, in this triangle?

NOT 4^2-b^2=5^2

Which equation can be used to find the unknown length, a, in this triangle?

a

In centimeters, what is the unknown length in this right triangle?

11

The repeating decimal, , is converted to the fraction .What is the value of x in the fraction?

11

Carlos found that the length of the diagonal of his laptop monitor is . If the manufacturer rounds to the nearest whole inch, what size is the monitor as measured by the diagonal? 12 17 97 245

17

What is the distance between the points (7, 8) and (-8, 0) on a coordinate grid?

17

A diagonal of a cube measures 30 inches. The diagonal of a face measures inches. In inches, what is the length of an edge of the cube? Round the answer to the nearest tenth. inches

17.2

A wire that is 22 feet long connects the top of a pole to the ground. The wire is attached to the ground at a point that is 10 feet from the base of the pole. What is the height of the pole? Round to the nearest hundredth. 12.00 feet 19.60 feet 24.17 feet 38.40 feet

19.60

How many repeating digits are in 0.536 repeating 1 2 3 4

3

Which triangle side lengths form a right triangle? Choose all that apply. 5, 6, 7 6, 8, 14 8, 15, 17 10, 12, 15 15, 20, 25 16, 18, 20

3 and 5

What is the length of given that is 2.5 inches and is inches? Round to the nearest tenth. 3.5 inches 8.8 inches 9.1 inches 10.8 inches

3.5

How much longer is the hypotenuse of the triangle than its shorter leg? 2 ft 4 ft 8 ft 10 ft

4ft

In a right triangle, the hypotenuse has endpoints P(-3, 2) and Q(1, -3).If R represents the third vertex in the triangle and R is located in the third quadrant, what is the length of PR? 3 4 5 6

5

Joseph and Isabelle left Omyra's house at the same time. Joseph jogged north at 8 kilometers per hour, while Isabelle rode her bike west at 12 kilometers per hour. Omyra tried to figure out how far apart they were after 1.5 hours. Her work is shown below. Which statements describe her errors? Check all that apply. She did not find the full distance each traveled in 1.5 hours. She should have used 12 km for Joseph's distance and 18 km for Isabelle's distance. She did not square the 12 in the problem. She should have used . She did not evaluate correctly. She should have used . She did not evaluate correctly. She should have used . She should not have taken the square root of each side when solving. She should have just divided each side by 2. She should not have added the squares in the first step. She should have used .

A She did not find the full distance each traveled in 1.5 hours. She should have used 12 km for Joseph's distance and 18 km for Isabelle's distance. b. She did not square the 12 in the problem. She should have used 12^2 =144

Lewis needed to find the difference in lengths between the hypotenuse and the longest leg of this triangle. His work is shown below.What errors did Lewis make? Check all that apply. He simplified incorrectly. It should be 20 instead of 200. He found the difference between the hypotenuse and the short leg instead of the long leg. He evaluated incorrectly. It should be . He evaluated incorrectly. It should be . He should not have taken the square root of each side to get rid of the exponent.

A.He simplified incorrectly. It should be 20 instead of 200. B. He found the difference between the hypotenuse and the short leg instead of the long leg.

Carl is trying to determine the length of segment MN using the Pythagorean theorem. Step 1: Find the vertex of a possible right triangle. V(4, 1)Step 2: Find the leg lengths of the right triangle. NV = 7, MV = 5Step 3: Substitute the values into the Pythagorean theorem. Step 4: Solve for c. Which best describes the accuracy of Carl's solution? Carl's work and answer are both entirely correct. Carl's answer is correct, but he incorrectly labeled the leg lengths in step 2. Carl's work and answer are incorrect. He choose a vertex, V, that does not make a right triangle with MN. Carl's work and answer are incorrect. He substituted and solved incorrectly.

Carl's answer is correct, but he incorrectly labeled the leg lengths in step 2.

Hassan used the iterative process to locate on the number line. Which best describes Hassan's estimation? Hassan is correct because Hassan is correct because the point is on the middle of the number line. Hassan is incorrect because is less than 0.4. Hassan is incorrect because the point should be located between 0.1 and 0.2.

Hassan is incorrect because is less than 0.4.

A ladder that is 14 feet long is placed against a building. The bottom of the ladder is 6 feet from the base of the building. In feet, how high up the side of the building is the top of the ladder? Round to the nearest tenth of a foot.

NOT 13.3

A diagonal of a cube measures cm. The diagonal of a face measures 10 cm. What is the length, in centimeters, of an edge of the cube? Round the answer to the nearest tenth. centimeters

NOT 15.8

Segment KJ shown below is the hypotenuse of isosceles right triangle JLK. What is the length of one of the congruent legs of JLK? 3 6

NOT 3

Keith left his house, rode his bike 3 miles along one road, took a 90 degree turn, and rode 3 miles to the local swimming pool. If he had ridden directly to the pool, how much distance would he have saved? Round the answer to the nearest tenth of a mile. 1.2 miles 1.8 miles 2.5 miles 4.2 miles

NOT D

What is the length of the unknown leg in the right triangle? 8 yd yd 64 yd yd

NOT D

The sum of a rational number and an irrational number equals: a terminating decimal. a rational number. a fraction. an irrational number.

NOT a fraction

What is the length of a diagonal of a cube with a side length of 10 cm? cm cm cm cm

NOT square root of 200

Which is a right triangle formed using a diagonal through the interior of the cube? triangle ABE triangle ABD triangle ADH triangle ACE

NOT triangle ADH

Which triangle has hypotenuse ? triangle BAE triangle CAE triangle GAE triangle HAE

NOT triangle BAE

Sanjay, Colby, and Arpitha are training to run a marathon. On Saturday, Sanjay ran miles, Colby ran 13 miles, and Arpitha ran the shortest route from the library to her house, as shown in the diagram. Which list shows the names in order from the person who ran the shortest distance to the one who ran the greatest distance? Colby, Sanjay, Arpitha Sanjay, Arpitha, Colby Sanjay, Colby, Arpitha Arpitha, Sanjay, Colby

NOt B

Imara used these steps to find the length of the hypotenuse of the right triangle.Step 1: Find the area of the square with side lengths of 20: 400 Step 2: Find the area of the square with side lengths of 15: 225Step 3: Find the sum of the areas of the two squares: 625Step 4: State the length of the hypotenuse: 625Which best describes Imara's error? She should have found the area of the square with side lengths of 15 first. She did not correctly calculate the area of the square with side lengths of 15. She should have found the sum of 15 and 20 and then squared the sum. She did not find the side lengths of the square with an area of 625.

She did not find the side lengths of the square with an area of 625.

Nadia says the hypotenuse of this right triangle has a length of 73 because the Pythagorean theorem states that .Which best describes Nadia's solution? She is correct because she applied the Pythagorean theorem properly and her arithmetic is accurate. She is incorrect because she should have used 45 as the length of the hypotenuse. She is incorrect because she should have squared each leg length and then found the sum. She is correct because the hypotenuse is the longest side of the triangle.

She is incorrect because she should have squared each leg length and then found the sum.

Holly and Tamar completed the work in the table to determine if a triangle with side lengths of 40, 42, and 58 is a right triangle. Holly's WorkTamar's WorkThe triangle is not a right triangle. The triangle is a right triangle. Which best describes the accuracy of their solutions? Holly is correct. Tamar is correct. Neither Holly nor Tamar is correct. Both Holly and Tamar are correct.

Tamar is correct.

Which statements are true? Select the two correct answers. The square root of a positive number greater than 1 is less than the number. The square root of a positive number is always less than half of the number itself. The square root of a positive number less than 1 is less than the number. The square root of a perfect square is not a whole number. The square root of a positive number less than 1 is between 0 and 1.

The square root of a positive number greater than 1 is less than the number. The square root of a positive number less than 1 is between 0 and 1.

Which statement describes whether a right triangle can be formed using one side length from each of these squares? Yes, a right triangle can be formed because the sum of the areas of the two smaller squares does not equal the area of the largest square. Yes, a right triangle can be formed because the sum of the areas of the two smaller squares equals the area of the largest square. No, a right triangle cannot be formed because the sum of the areas of the two smaller squares does not equal the area of the largest square. No, a right triangle cannot be formed because the sum of the areas of the two smaller squares equals the area of the largest square.

Yes, a right triangle can be formed because the sum of the areas of the two smaller squares equals the area of the largest square.

Ilya builds a slide that is 2.9 meters long. It is 1.5 meters above the ground. He wants to determine the distance from the bottom of the slide to the base of the ladder leading up to the slide. Which diagram represents this situation?

a

Jackie plans to place a rectangular piece of art inside a rectangular frame. She considers a piece of art that is 0.5 meters long, 1.2 meters wide, and has a diagonal length of 1.3 meters.Which is true regarding the art piece? The art is rectangular because . The art is rectangular because . The art is not rectangular because . The art is not rectangular because .

a

Tasha assembled a picture frame that is advertised as rectangular. The completed frame is 14 inches long and 10 inches wide. She measured the diagonal length across the frame as 20 inches. Which best explains why the frame cannot actually be rectangular?

a

The hypotenuse of right triangle ABC is represented by segment AB, as shown on the graph. At which point could point C be located? (-3, 3) (-3, 2) (5, -5) (5, -3) Submitted

a

Two students are using the distance formula to determine the distance between (9, 4) and (-3, 8) on a coordinate grid. Their work is shown below. Karlin's WorkAbby's WorkWhich best explains why the order in which the subtraction occurred did not cause a difference in the answers determined by the two girls? The differences are each squared. The differences are added together. The square root of the differences is taken. The differences are the same regardless of order.

a

Which equation can be used to find the unknown length, b, in this triangle?

a

Which expression can be used to determine the length of segment AB?

a

Which expression represents the distance between point (0, a) and point (a, 0) on a coordinate grid? 0

a

Segment KJ shown below is the hypotenuse of isosceles right triangle JLK. What is the length of one of the congruent legs of JLK? 3 6

b

Tyree is determining the distance of a segment whose endpoints are A(-4, -2) and B(-7, -7).Step 1: Step 2: Step 3: Step 4: Step 5: Therefore, d = 2.Which best describes the accuracy of Tyree's solution? Tyree's solution is accurate. Tyree's solution is inaccurate. In step 1, he substituted incorrectly. Tyree's solution is inaccurate. In step 2, he simplified incorrectly. Tyree's solution is inaccurate. In step 3, he added incorrectly.

b

Which expression represents the distance between the points (a, 0) and (0, 5) on a coordinate grid?

b

What is the length of a diagonal of a cube with a side length of 1 cm? cm cm cm cm

b square root of 3 cm

Kendra is determining the distance between the points (6, 8) and (2, -3). Her work is shown below. Step 1: Step 2: Step 3: Step 4: Which best describes the accuracy of Kendra's solution? Her solution is correct. Her solution is incorrect. She subtracted before squaring. Her solution is incorrect. She made an error when substituting the x-values into the equation. Her solution is incorrect. She made an error when substituting the y-values into the equation.

d

Giselle is building a small baseball infield for her brother. The infield should be in the shape of a square. Each side of the infield, between bases, measures 30 feet. The distance between home plate and second base, as shown in the picture, is 45 feet. Which best describes the shape of the baseball field? Square: Not square: Not square: Not square:

not square: 2(30)^2 not equal to 45^2

Which statements are true? Select the two correct answers. The square root of a positive number greater than 1 is less than the number. The square root of a positive number is always less than half of the number itself. The square root of a positive number less than 1 is less than the number. The square root of a perfect square is not a whole number. The square root of a positive number less than 1 is between 0 and 1.

not these two together The square root of a positive number greater than 1 is less than the number. The square root of a positive number less than 1 is less than the number.

Which of these four sets of side lengths will form a right triangle?Set 110 cm, 26 cm, 24 cmSet 24 in., 2 in., 6 in.Set 314 mm, 13 mm, 15 mmSet 410 ft, 30 ft, 20 ft Set 1 Set 2 Set 3 Set 4

step 1

Which triangle has hypotenuse ? triangle BFE triangle BFH triangle BFD triangle BFG

triangle BFG

Which triangle has hypotenuse ? triangle AFG triangle BFG triangle EFG triangle DFG

triangle EFG

Which triangle has hypotenuse ? triangle ACH triangle BCH triangle GCH triangle FCH

triangle GCH

Which is a right triangle formed using a diagonal through the interior of the cube? triangle BDH triangle DCB triangle GDC triangle GHE

triangle GDC

James cut out four parallelograms, the dimensions of which are shown below. Parallelogram 1length: 12 in.width: 15 in.diagonal: 20 in.Parallelogram 2length: 16 in.width: 30 in.diagonal: 34 in.Parallelogram 3length: 20 in.width: 21 in.diagonal: 29 in.Parallelogram 4length: 18 in.width: 20 in.diagonal: 26 in.James put the parallelograms together so one vertex from each paper exists on a point, as shown in the circle.Which statement explains whether or not the parallelgrams can be put together so each occupies one-quarter of the area of the circle without overlapping any other pieces? Check all that apply. The quadrilaterals can be placed such that each occupies one-quarter of the circle. The quadrilaterals cannot be placed such that each occupies one-quarter of the circle because the vertices of parallelogram 1 do not form right angles. The quadrilaterals cannot be placed such that each occupies one-quarter of the circle because the vertices of parallelogram 2 do not form right angles. The quadrilaterals cannot be placed such that each occupies one-quarter of the circle because the vertices of parallelogram 3 do not form right angles. The quadrilaterals cannot be placed such that each occupies one-quarter of the circle because the vertices of parallelogram 4 do not form right angles.

2 and 5

A ladder that is 21 feet long is propped against a building. The bottom of the ladder was placed 4 feet from the base of the building. How high up on the building does the ladder reach? Round the answer to the nearest tenth of a foot. 4.1 feet 17.0 feet 20.6 feet 21.4 feet

20.6 ft

Every weekday, Mr. Jones bikes from his home to his job. Sometimes he rides along two roads, the long route that is shown by the solid lines. Other times, he takes the shortcut shown by the dashed line. How many fewer kilometers does Mr. Jones bike when he takes the shortcut instead of the long route? 6 kilometers 8 kilometers 23 kilometers 32 kilometers

6 kilometers

Arnob may want to borrow his cousin's tent, which is shown below.He needs to determine x, the center height of the tent, to determine if it will be large enough for his camping trip. What is the center height of this tent, to the nearest tenth of a foot? 4.1 feet 8.1 feet 9.8 feet 12.0 feet

8.1

Arnob may want to borrow his cousin's tent, which is shown below.He needs to determine x, the center height of the tent, to determine if it will be large enough for his camping trip. What is the center height of this tent, to the nearest tenth of a foot? 4.1 feet 8.1 feet 9.8 feet 12.0 feet

8.1 ft

Mrs. Ibarra wants to create a right triangle for a geometry test. She plans to use 15, 36, and 41 as side lengths. Which statements should she consider to determine whether it will be a right triangle? Check all that apply. , so the side lengths will form a triangle. , so those lengths will not form a triangle. Since , it will not be a right triangle.

A. 15+36>41, so the side lengths will form a triangle C.15^2+36^2=1521 D.41^2=1681 E.since a^2+b^2 not equal it will not be a right triangle

Jeremy is trying to explain why a triangle with side lengths 35, 30, 60 is not a right triangle. His explanation is shown below.Step 1: Step 2: Step 3: Step 4: Which best describes Jeremy's explanation? Jeremy's explanation is accurate. Jeremy's explanation is inaccurate. He wrote the leg lengths in the incorrect order in step 1. Jeremy's explanation is inaccurate. He incorrectly combined terms in step 2. Jeremy's explanation is inaccurate. He multiplied incorrectly in step 4.

Jeremy's explanation is inaccurate. He incorrectly combined terms in step 2.

James cut out four parallelograms, the dimensions of which are shown below. Parallelogram 1length: 12 in.width: 15 in.diagonal: 20 in.Parallelogram 2length: 16 in.width: 30 in.diagonal: 34 in.Parallelogram 3length: 20 in.width: 21 in.diagonal: 29 in.Parallelogram 4length: 18 in.width: 20 in.diagonal: 26 in.James put the parallelograms together so one vertex from each paper exists on a point, as shown in the circle.Which statement explains whether or not the parallelgrams can be put together so each occupies one-quarter of the area of the circle without overlapping any other pieces? Check all that apply. The quadrilaterals can be placed such that each occupies one-quarter of the circle. The quadrilaterals cannot be placed such that each occupies one-quarter of the circle because the vertices of parallelogram 1 do not form right angles. The quadrilaterals cannot be placed such that each occupies one-quarter of the circle because the vertices of parallelogram 2 do not form right angles. The quadrilaterals cannot be placed such that each occupies one-quarter of the circle because the vertices of parallelogram 3 do not form right angles. The quadrilaterals cannot be placed such that each occupies one-quarter of the circle because the vertices of parallelogram 4 do not form right angles.

NOT 1 and 4 together The quadrilaterals can be placed such that each occupies one-quarter of the circle. The quadrilaterals cannot be placed such that each occupies one-quarter of the circle because the vertices of parallelogram 3 do not form right angles.

The areas of the squares created by the side lengths of the triangle are shown. Which best explains whether this triangle is a right triangle?[Not drawn to scale] Based on the converse of the Pythagorean theorem, the triangle is a right triangle because . Based on the converse of the Pythagorean theorem, the triangle is not a right triangle because . Based on the converse of the Pythagorean theorem, the triangle is not a right triangle because . Based on the converse of the Pythagorean theorem, the triangle is not a right triangle because .

NOT A

Pedro, Lena, Harriet, and Yermin each plot a point to approximate .PedroLenaHarrietYerminWhose point is the best approximation of ? Pedro Lena Harriet Yermin

Yermin

Hans wanted to find the length of the hypotenuse of the triangle. Which statement correctly identifies his error? He did not square 40, he just multiplied by 2. He did not finish the problem. He should have divided 161 by 2 to find the square root. He should have added 9 + 9 to find the value of . He should have subtracted the two squares to get because numbers get too large if both legs are squared and then added together.

a

Alyssa is jogging near Central Park. She runs along 65th Street for about 0.19 miles, turns right and runs along Central Park West for about 0.28 miles. She then turns right again and runs along Broadway until she reaches her starting point. How long is her total run to the nearest hundredth of a mile? 0.68 miles 0.81 miles 1.15 miles 1.44 miles

b

In an isosceles triangle, the longest side measures c units. The other sides of the triangle measure a units. Which equation can be used to determine if the triangle is a right triangle?

b

Jude is making a door for a door frame with an opening that measures 9 feet by 3 feet. Which diagonal length should he use to make a door that fits in the door frame? 10 feet feet feet 12 feet

b

Keith left his house, rode his bike 3 miles along one road, took a 90 degree turn, and rode 3 miles to the local swimming pool. If he had ridden directly to the pool, how much distance would he have saved? Round the answer to the nearest tenth of a mile. 1.2 miles 1.8 miles 2.5 miles 4.2 miles

b

Samantha and Mia each left Julia's house at the same time. Mia walked north at 7 kilometers per hour. Samantha ran west at 11 kilometers per hour. How far apart were they after one hour? Round the answer to the nearest tenth. 7.7 km 8.4 km 13.0 km 18.0 km

c

Which best explains why this triangle is or is not a right triangle? This triangle is not a right triangle: . This triangle is not a right triangle: . This triangle is a right triangle: . This triangle is a right triangle: .

d

What is the length of the hypotenuse of the triangle? cm cm cm cm

d Is radicle 58cm

Jana is ordering a list of numbers from least to greatest.Which statement can be used to create her list? is less than because and the square root of a number less than 1 is less than the number itself. is greater than because and the square root of a number greater than 1 is greater than the number itself. is less than because and is between 6 and 8. is greater than because is less than 1 and the square root of a number greater than 1 is greater than 1.

is greater than because is less than 1 and the square root of a number greater than 1 is greater than 1.

Nolan used the following procedure to find an estimate for .Step 1: Since and and 16 < 18 < 25, is between 4 and 5.Step 2: Since 18 is closer to 16, square the tenths closer to 4.Step 3: Since 18.49 rounds to 18, 4.3 is the best approximation for .In which step, if any, did Nolan make an error? In step 1, is between 4 and 5 because 20 and . In step 2, he made a calculation error when squaring. In step 3, he should have determined which square is closest to 18. Nolan did not make an error.

not Nolan did not make an error.

What is the length of the hypotenuse of the triangle? ft ft ft ft

radicle 65 ft

Which of these four sets of side lengths will form a right triangle?Set 16 cm, 7 cm, cmSet 28 in., in., in.Set 3 mm, 4 mm, mmSet 49 ft, ft, 6 ft Set 1 Set 2 Set 3 Set 4

set 2

Which of these four sets of side lengths will form a right triangle?Set 14 cm, 5 cm, 6 cmSet 2 8 in., 12 in., 20 in.Set 310 mm, 20 mm, 30 mmSet 412 ft, 16 ft, 20 ft Set 1 Set 2 Set 3 Set 4

set 4