Geometry

Analyze the diagram below and complete the instructions that follow. In the diagram shown above, ABCD is a parallelogram. The ratio of the area of AGB to the area of CGE is 9:25. If CG = 10 and GE = 15, find GB.

GB=9

Analyze the diagram below and complete the instructions that follow. Determine which 2 triangles are similar to each other. The images are not drawn to scale.

GHI ~ JKL

Analyze the diagram below and complete the instructions that follow. Given that FG//HI, FJ = 6, FG = 8, HJ = 10, and IJ = 15, find GJ and HI.

GJ = 4, HI = 20

In quadrilateral HELP, <HEP=<LPE. What other condition would prove that HELP is a parallelogram?

HE=LP

Analyze the diagram below and complete the instructions that follow. Square 1 has a side length of x, and square 2 has a side length of y. Square 2 is formed by joining the midpoints of the sides of square 1 in order. If x = 2, find the ratio of the area of square 1 to the area of square 2.

2:1

Analyze the diagram below and complete the instructions that follow. Find the value of a.

3

Analyze the diagram below and complete the instructions that follow. Pentagon PQRST ~ pentagon XYZVW. Find the value of b. The images are not drawn to scale.

3

Find an integer, x, such that 2, 4, and x represent the lengths of the sides of an obtuse triangle.

3

Analyze the proportion below and complete the instructions that follow. 2/3 = 8/x

3, 8

Analyze the diagram below and complete the instructions that follow. Find the ratio of the width to the length of the rectangle, then simplify the ratio. Use the conversion 100 cm = 1 m.

3/4

Analyze the diagram below and complete the instructions that follow. Find cos<C

3/5

Analyze the diagram below and complete the instructions that follow. Find sin<NOM

3/5

Find sin<NOM

3/5

If 14/3 = x/y then 14/x =

3/y

ABCD is an isosceles trapezoid with diagonals that intersect at point P. If AB||CD, AC = 7y - 30, BD = 4y + 60, and CD = 5y + 14, solve for y.

30

Analyze the diagram below and complete the instructions that follow. Find the value of x.

30

If a+b/2a-b = 5/4 and b/a+9 = 5/9, find the value of b.

30

Parallelogram PQRS is shown. m<S= (3x), m<R= 120, and <Q= (2y). Find the value of y.

30

Given that XW/XV = YW/ZV, find ZV.

34

Analyze the diagram below and complete the instructions that follow. The diagram shows corresponding lengths in two similar figures. Find the area of the smaller figure.

36 cm2

A yardstick casts a shadow of 24 in. at the same time a telephone pole casts a shadow of 20 ft 8 in. What is the height of the telephone pole, to the nearest inch? (1 yd = 36 in., and 1 ft = 12 in.)

372 in.

Given that HIJK is a paralleogram, find m<I.

37°

Given that JKLM is a rhombus, find m<3.

37°

The area of LMN is 18 ft2, and the area of FGH is 32 ft2. If LMN~FGH, what is the ratio of LM to FG?

3:4

Analyze the diagram below and complete the instructions that follow. Find the value of x.

3√2 / 2

Which of the following could be the lengths of the sides of a 45°-45°-90° triangle?

3√2, 3√2, 6

Analyze the diagram below and complete the instructions that follow. Find the exact value of tan 0

3√5 / 5

Find the geometric mean of 7 and 9.

3√7

Analyze the diagram below and complete the instructions that follow. Find the value of x.

4

Find an integer, x, such that 2, 4, and x represent the lengths of the sides of an acute triangle.

4

Find the value of f for which MATH is a parallelogram.

4

The diagonals of parallelogram LMNO, LN and MO, intersect at point P. If LP= 7, MP= 5x-10 and OP= 2x+2, solve for x.

4

Analyze the diagram below and complete the instructions that follow. Find tan<E

4/3

Analyze the diagram below and complete the instructions that follow. Find cos<FHE

4/5

Analyze the diagram below and complete the instructions that follow. Find sin<A

4/5

ABCD is an isosceles trapezoid. If AD||BC, m<B=(x+10) and m<C=(2x-30), solve for x.

40

The given lengths are two sides of a right triangle. All three side lengths of the triangle are integers, and together they form a Pythagorean triple. Find the length of the third side, then indicate whether it is a leg or a hypotenuse. 75, 85

40, leg

Analyze the diagram below and complete the instructions that follow. In the figure, AB//CD. If ED:EA = 14:9 and the perimeter of BEA is 27, find the perimeter of CED.

42

The diagonals of quadrilateral ABCD intersect at point E, AE= 5x - 10, EC= 2x + 5, and BE = y/3. If ABCD is a square, find the value of y.

45

Analyze the diagram below and complete the instructions that follow. Jessica is trying to win this game of pool. She needs to hit the cue ball (white ball) 10 in. into the yellow ball so it will travel 15 in. to bounce off the back wall, travel across the table, and then land in the pocket. Determine the distance (d) that the yellow ball must travel after hitting the back wall to land in the pocket.

45 in.

Analyze the diagram below and complete the instructions that follow. Find the value of z. Round the answer to the nearest tenth, if needed.

45.6

What type of special right triangle can an isosceles triangle be?

45°-45°-90°

Quadrilateral ABCD is a square with diagonals that intersect at point E. Find m<ADB.

45º

Analyze the diagram below and complete the instructions that follow. The diagram shows corresponding lengths in two similar figures. Find the ratio of the areas of the two figures.

49:81

If the ratio of the areas of two similar polygons is 32:50, what is the ratio of the corresponding side lengths?

4:5

Analyze the diagram below and complete the instructions that follow. If ON = MN, find MN.

4√2

Analyze the diagram below and complete the instructions that follow. Find the unknown side length, x. Write your answer in simplest radical form.

4√37

Analyze the diagram below and complete the instructions that follow. If √61 is the longest side length in the triangle, find the value of x that makes the triangle above a right triangle. Write your answer in simplest radical form.

5

The altitude to the hypotenuse of a right triangle divides the hypotenuse into segments of lengths 5 and 15. What is the length of the altitude?

5 √3

Analyze the diagram below and complete the instructions that follow. Find cos<C

5/13

Analyze the diagram below and complete the instructions that follow. Find sin<L

5/13

If 5/y + 7/x=24 and 12/y + 2/x=24, find the ratio of x to y.

5/7

Analyze the diagram below and complete the instructions that follow. Find the value of z.

50

Analyze the diagram below and complete the instructions that follow. Solve for x.

52/3

The diagonals of kite KITE intersect at point P. If m<TIE= 53, m<KTE= 2x, and m<TEI= 38, find m<KTE.

52°

Analyze the diagram below and complete the instructions that follow. Find the height of the roof.

53.7 cm

Analyze the diagram below and complete the instructions that follow. Solve for x.

1

Find tan(Q)

1

Simplify the ratio 3 gal./24 qt. Use the conversion 4 qt = 1 gal.

1/2

Given that cos(x) = 1/3, find sin (90-x)

1/3

Analyze the diagram below and complete the instructions that follow. Find the value of x.

10

Quadrilateral ABCD is an isosceles trapezoid. If AB||CD, AB = m + 6, CD = 3m + 2, BC = 3m, and AD = 7m - 16, find AB.

10

Quadrilateral WXYZ is a rectangle. The perimeter of XYZ is 24, XY+YZ= 5x - 1 and XZ= 13 - x. Find the length of WY

10

The sides of a triangle have lengths of x, x + 4, and 20. If the longest side is 20, which of the following values of x would make the triangle obtuse?

10

Analyze the diagram below and complete the instructions that follow. Given that CB/CA = DE/DF, find BA.

10.5

Quadrilateral ABCD is a square with diagonals that intersect at point E. Find the perimeter of ABCD.

100

Quadrilateral LMNO is a rectangle. Find the perimeter of LMNO. The figure is not drawn to scale.

102

Given that JKLM is a rhombus, find m<KJM

106°

Find an integer, x, such that 5, 10, and x represent the lengths of the sides of an acute triangle.

11

Using Pythagorean inequalities, determine which of the following sets of values could represent the lengths of the sides of an obtuse triangle.

11, 12, 22

Which of the following is not a Pythagorean triple?

11, 61, 62

A 12-foot ladder rests against the side of a house. The base of the ladder is 3 feet away from the side of the house. How high above the ground is the top of the ladder? Round to the nearest tenth of a foot.

11.6 feet

Find the unknown side length, x. Write your answer in simplest radical form.

11√2

In a 45°-45°-90° triangle, the length of the hypotenuse is 11. Find the length of one of the legs.

11√2 / 2

Quadrilateral ABCD is an isosceles trapezoid. If AB||CD, AB = m + 6, CD = 3m + 2, BC = 3m, and AD = 7m - 16, find BC.

12

The length of a rectangular painting is 3 inches longer than its width. If the diagonal is 15 inches long, what is the length of the painting?

12 inches

Analyze the diagram below and complete the instructions that follow. Find tan<C

12/5

ABCD is an isosceles trapezoid. If AD||BC, m<B= 60, and m<C= (3x+15), find the measure of <A.

120°

Rhombus BOXY has angle measures as shown in the diagram. Find the measure of <B.

120°

In parallelogram MATH, m<M= (3x+20) and m<T= (5x-4). Find m<A.

124°

In baseball, the length of the path between each pair of consecutive bases is 90 feet. The paths form right angles. How far does the ball need to travel if it is thrown from home plate directly to second base?

127.3 feet

Analyze the diagram below and complete the instructions that follow. Find the height of the basketball hoop to the nearest foot.

12ft

ABCD is an isosceles trapezoid. If AD||BC, m<B= (x+10), and m<C= (2x-30), find the measure of <D.

130°

Analyze the diagram below and complete the instructions that follow. The diagram shows corresponding lengths in two similar figures. Find the area of the smaller figure.

135 cm2

If the hypotenuse of a 45°-45°-90° triangle is 13, what is the length of one of the legs?

13√2 / 2

The sides of a triangle have lengths of x, x + 4, and 20. If the longest side is 20, which of the following values of x would make the triangle acute?

14

Analyze the diagram below and complete the instructions that follow. The diagram shows corresponding lengths in two similar figures. Find the area of the smaller figure.

14.4 yd2

Given that HIJK is a parallelogram, find m<J.

143°

Analyze the diagram below and complete the instructions that follow. Median MH is 6 units longer than median KP. Triangle GHI is similar to triangle JKL. If GH:JK= 7:5, find the length of KP.

15

In a 30°-60°-90° triangle, the length of the hypotenuse is 30. Find the length of the shorter leg.

15

The sides of a triangle have lengths of x, x + 5, and 25. If the longest side is 25, which of the following values of x would make the triangle right?

15

A new patio will be an irregular hexagon. The patio will have two long parallel sides and an area of 360 square feet. The area of a geometrically similar patio is 250 square feet, and its long parallel sides are 12.5 feet apart. What is the corresponding distance on the new patio?

15 feet

Analyze the diagram below and complete the instructions that follow. Use the given area to find XY.

15 in.

Find m<K.

150°

Analyze the diagram below and complete the statement that follows. If GHI~JKL, JP = 35, MH=33, and PK=15, then GI=

154

ABCD is an isosceles trapezoid. If AB||CD, AC = 3x - 12, and BD = 2x + 4, solve for x.

16

In quadrilateral ABCD, m<B= 11, m<C= 95, and m<D= 90. Find the measure of <A.

164°

Analyze the diagram below and complete the instructions that follow. Find the unknown side length, x. Write your answer in simplest radical form.

16√5

Analyze the diagram below and answer the question that follows. What is the largest integer value of MO for which rhombus MNOP will have an obtuse angle at P?

17

Quadrilateral ABCD is an isosceles trapezoid with AB||CD. If BC = 4x + 5 and AD = -3x + 26, find AD.

17

The area of a rectangle is 1,872 ft2. The ratio of the length to the width is 9:13. Find the perimeter of the rectangle.

176 ft

Analyze the diagram below and complete the instructions that follow. Find the value of x.

18

Given that EFGH is a kite, if FG=HG, find HG.

18

Quadrilateral ABCD is a square. If m<DCB= 5x, find x.

18

The diagonals of parallelogram LMNO, LN and MO, intersect at point P. If LP= 6 and NP= x/3 solve for x.

18

You want to make a scale drawing of your bedroom to help arrange your furniture. You decide on a scale of 3 in. = 2 ft. Your bedroom is a 12 ft by 14 ft rectangle. What should the dimensions of your drawing be?

18 in. by 21 in.

The diagonals of parallelogram QRST, TR and QS, intersect at point U. If RS = 10, ST = 12, and RU = 9.5, find the length of RT.

19

Analyze the diagram below and complete the instructions that follow. Find the value of x.

2

Parallelogram PQRS is shown. m<S= (3x), m<R= 120, and <Q= (2y). Find the value of x.

20

The diagonals of parallelogram LMNO, LN and MO, intersect at point P. If LP= 7, MP= 5x-10 and OP= 2x+2, find MO

20

The diagonals of rhombus WXYZ intersect at point P. If WP = 4 and ZP = 3, find the perimeter of the rhombus.

20

Analyze the diagram below and complete the instructions that follow. Find the length of AB.

21

Analyze the diagram below and complete the instructions that follow. Median MH is 6 units longer than median KP. Triangle GHI is similar to triangle JKL. If GH:JK = 7:5, find the length of MH.

21

Figure ABCD is a kite. If AD=AB, find AB.

22

Quadrilateral ABCD is a kite. If AD=AB, find AD.

22

ABC is a right triangle. The legs of ABC are 9 ft and 12 ft. The shortest side of XYZ is 13.5 ft, and ABC ~ XYZ How long is the hypotenuse of XYZ?

22.5 ft

Analyze the diagram below and complete the instructions that follow. Find the value of y.

24

Analyze the diagram below and complete the instructions that follow. Given that AB//CD, find the value of x.

24

Analyze the diagram below and complete the instructions that follow. If ABC ~ XYZ, find XY. The images are not drawn to scale.

24

Analyze the diagram below and complete the instructions that follow. In the diagram, AB:BC is 3:4 and AC = 42. Find BC.

24

Find the geometric mean of 6 and 96.

24

Given that ABCD is a rhombus, find x.

24

Squares MNPQ and RSTU are similar. The ratio of their areas is 16:9. If the larger square has a side length of 8 inches, what is the perimeter of the smaller square?

24 inches

Find the value of t for which WXYZ is a parallelogram.

25

Given that LMNO is a parallelogram, solve for t.

25

The diagonals of kite KITE intersect at point P. If m<TIE= 53, m<KTE= 2x, and m<TEI= 38, solve for x.

26

Analyze the diagram below and complete the instructions that follow. Find the value of y. Round the answer to the nearest tenth, if needed.

27

Quadrilateral WXYZ is a rectangle. The perimeter of XYZ is 24, XY+YZ= 5x - 1 and XZ= 13 - x. Find the perimeter of WXYZ.

28

The diagonals of kite KITE intersect at point P. If m<TKE= (x+6), and m<IEK= 2x, solve for x.

28

Analyze the diagram below and complete the instructions that follow. Find the value of y. Round the answer to the nearest tenth, if needed.

54

Analyze the diagram below and complete the instructions that follow. Find the length of the altitude to the hypotenuse. Round the answer to the nearest tenth, if needed.

56.8

In parallelogram MATH, m<M= (3x+20) and m<T= (5x-4), Find m<M.

56°

The diagonals of kite KITE intersect at point P. If m<TKE= (x+6), and m<IEK= 2x, find m<KEI

56°

Analyze the diagram below and complete the instructions that follow. Find the unknown side length, x. Write your answer in simplest radical form.

58

Analyze the ratio below and complete the instructions that follow. $30:$6 Simplify the ratio.

5:1

Analyze the diagram below and complete the instructions that follow. Find the unknown side length, x. Write your answer in simplest radical form.

5√10

Analyze the diagram below and complete the instructions that follow. In this rectangular box, EF = 6, FD = 5, and DB = 8. Find AF.

5√5

Analyze the diagram below and complete the instructions that follow. Find the value of x. Round the answer to the nearest tenth, if needed.

6

Find an integer, x, such that 5, 10, and x represent the lengths of the sides of an obtuse triangle.

6

Find the value of g for which MATH is a parallelogram.

6

Analyze the diagram below and complete the instructions that follow. Solve for x.

6.4

Given the diagram of parallelogram LMNO, find m<M.

60°

Find m<D.

61

Analyze the diagram below and complete the instructions that follow. Find the unknown side length, x. Write your answer in simplest radical form.

65

Analyze the diagram below and answer the question that follows. 17th Street, 18th Street, 19th Street, and 20th Street are parallel streets that intersect 1st Avenue and 2nd Avenue. How long is 2nd Avenue between 18th Street and 17th Street, to the nearest foot?

671 ft

ABCD is a quadrilateral. Three of the angles of ABCD measure 100°, 87°, and 106°, respectively. Find the measure of the missing angle.

67°

The diagonals of kite KITE intersect at point P. If m<KIP= 46, and m<KEP= 34, find <KET

68

The diagonals of kite KITE intersect at point P. If <TKE= (x+6) and m<IEK= 2x, find m<IKE.

68°

Given that ABCD is a parallelogram, solve for k.

7

Quadrilateral ABCD is a kite. If AD=AB, solve for x.

7

Quadrilateral ABCD is a parallelogram with AB = 3y - 6, BC = 5x - 8, CD = 2y + 4, and AD = 4x -1. Find x.

7

Quadrilateral WXYZ is a rectangle. If WY = 4x - 1 and XZ = 5x - 3, find the length of XZ

7

Given that sin(x)= 7/11, find cos (90 - x)

7/11

Quadrilateral ABCD has side lengths of AB = 13w - 5, BC = 5z - 2, CD = 13w - 5, and AD = 3z + 5. Find the value of z for which quadrilateral ABCD is a parallelogram.

7/2

Find m<A.

71°

The measures of the angles of a triangle are in the extended ratio 4:5:6. Find the measure of the largest angle in the triangle.

72

The area of a rectangle is 4,320 ft2. The ratio of the length to the width is 6:5. Find the length of the rectangle.

72 ft

In quadrilateral ABCD, if m<B= 95, m<C= 100, and m<D= 90 find the measure of <A

75°

Analyze the diagram below and complete the instructions that follow. Solve for x.

8

Given that ABCD is a parallelogram, solve for m.

8

Analyze the diagram below and complete the instructions that follow. Use the given area to find XY.

8 cm

Simplify the ratio 8ft/12in. Use the conversion 12 in. = 1 ft.

8/1

What is the length of a diagonal of a square with a side length of 8?

8√2

Analyze the diagram below and complete the instructions that follow. If AB:BC is 3:11, solve for x.

9

Given that JKLM is a rhombus, find m<1

90°

Analyze the diagram below and complete the instructions that follow. The figures shown above are similar. Find the perimeter of trapezoid GHIJ. The images are not drawn to scale.

93 units

Given that MATH is a parallelogram, solve for b.

96

Analyze the diagram below and complete the statement that follows. mA___mD

<

The diagonals of kite PQRS intersect at point T. Which statement is not true?

<QRS = <QPS

Complete the proof. Given: Parallelogram HIJK with diagonals intersecting at L Prove: <IKJ=HIK A. 2) Opposite sides in a parallelogram are congruent 3) Diagonals of a parallelogram bisect each other 4) SSS 5) CPCTC

A

Which of the following statements is true?

A square is a rhombus.

Analyze the diagram below and complete the instructions that follow. A student used the diagram above to set up the following proportion. Describe and correct this student's error.

D

Analyze the diagram below and complete the instructions that follow. Find sin(0)

DE/DF

Analyze the diagram below and answer the question that follows. Which side is opposite 0?

EF

Which of the following statements is not always true?

In a rhombus, all four angles are congruent.

Which of the following statements is not always true?

In a rhombus, the diagonals are congruent.

Which property makes a rectangle a special type of parallelogram?

The diagonals are congruent.

Given a rhombus, a square, and a rectangle, what must be true of all three quadrilaterals?

The diagonals bisect each other.

The figure shown is a rhombus. What condition would also make it a square?

The figure would be a square if the diagonals were congruent.

If m<ADC= 100, is ABCD a parallelogram? Explain.

Yes; the alternate interior angles are congruent, so AB||CD. Therefore, one pair of opposite sides is congruent and parallel.

Given the information below, find the coordinates of Z such that ABCD~WXYZ. A(-5, -1), B(-1, -1), C(-1, -5), D(-5, -5), W(2, 3), X(8, 3), Y(8, -3)

Z(2, -3)

The figure shown in this diagram could be __________.

a square, if the diagonals are congruent

Find the expression that represents the length of the hypotenuse of a right triangle whose legs measure m2 - n2 and 2mn

m2 + n2

Analyze the diagram below and complete the instructions that follow. Find the value of x and the value of y.

not enough information to determine

Which of the following ratios is used in finding the tangent of an angle in a right triangle?

opposite leg/adjacent leg

Analyze the diagram below and complete the instructions that follow. Find the value of x and the value of y.

x= 2√2, y=2√6

Analyze the diagram below and complete the instructions that follow. Find the value of x and the value of y.

x= 2√3 y=4√3

Analyze the diagram below and complete the instructions that follow. Find the value of x and the value of y.

x= 6√3 y=12

Analyze the diagram below and complete the instructions that follow. Find the value of x and the value of y.

x=7, y=4√2

Analyze the diagram below and complete the instructions that follow. Find the value of each of the variables.

x=9 , y=15 , z=20

Analyze the diagram below and complete the instructions that follow. Find the value of x and the value of y.

x=9√3, y=18

Find the value of y.

y= 4√3 / 3

Analyze the diagram below and complete the instructions that follow. Find sin 45.

√2 / 2

Analyze the diagram below and complete the instructions that follow. Find cos 45

√2 / 2

Using Pythagorean inequalities, determine which set of the given three sides produces an acute triangle.

√3 √4 √5

Which of the following could be the lengths of the sides of a 30°-60°-90° triangle?

√3, 3, 2√3

Analyze the diagram below and complete the instructions that follow. Find the unknown side length, x. Write your answer in simplest radical form.

√41

Find the geometric mean of 6 and 7.

√42

Analyze the diagram below and complete the instructions that follow. Find the unknown side length, x. Write your answer in simplest radical form.

√65

Analyze the proportion below and complete the instructions that follow. 2x+5/3 = x-5/4

-7

Find the value of x.

-9, 9

Analyze the diagram below and complete the instructions that follow. The triangles shown above are similar. Write the ratios of corresponding side lengths in a statement of proportionality. The images are not drawn to scale.

AB/ZX = BC/XY = CA/YZ

Analyze the diagram below and complete the instructions that follow. Identify the three similar right triangles in the given diagram.

ABD, ADC, DBC

Quadrilateral ABCD is an isosceles trapezoid with AB||CD. Which of the following is not true?

AC | BD

Quadrilateral ABCD is an isosceles trapezoid with AD||BC. Which of the following is not true?

AD = BC

Analyze the diagram below and complete the instructions that follow. In the diagram shown above, ABCD is a parallelogram. The ratio of the area of triangle AGB to the area of triangle CGE is 9:25. If CG = 10 and GE = 15, find AG.

AG = 6

Analyze the diagram below and complete the instructions that follow. Determine if the proportion is true. If it is not true, correct the error.

B

Analyze the diagram below and complete the instructions that follow. If ABC is similar to EFG, find BC and FH.

BC=12 FH=9

The area of LMN is 18 ft2 and the area of FGH is 24 ft2. If LMN~FGH, what is the ratio of LM to FG?

C - 3:2

Analyze the diagram below and answer the question that follows. In the diagram above, MN/MR = MP/MQ. Which statement must be true?

MNP ~ MRQ

Analyze the diagram below and answer the question that follows. Jeremy is going to help his neighbor build a patio similar in shape to his patio. Jeremy's neighbor's patio will have twice the area of Jeremy's patio. How can Jeremy use the dimensions of his patio to determine the dimensions of his neighbor's patio?

Multiply each dimension by 2.

You walk east 720 feet to get from your house to class. After class, you walk southwest 1,044 feet to meet your friends for lunch. When walking the 756 feet back home from lunch, what direction are you traveling?

N

Analyze the diagram below and answer the question that follows. Is ABC a right triangle? Why or why not?

No, ABC is not a right triangle, because AC would have to be 2√10

Analyze the diagram below and complete the instructions that follow. Is ABC a right triangle? Why or why not?

No, ABC is not a right triangle, because AC would have to be 2√74

Analyze the diagram below and answer the question that follows. Is QRS a right triangle? Why or why not?

No, QRS is not a right triangle, because QS would have to be √89

Summer said that it didn't matter which sides of a right triangle were a, b, and c. Is she correct?

No, a and b are interchangable, and c is the longest side.

Analyze the diagram below and complete the instructions that follow. Determine whether KM//JN. Explain.

No, because 18/10 = 24/15

Is the triangle with the given dimensions a right triangle? If so, which angle is the right angle? AB=10 BC=8 CA=5

No, it is not a right triangle.

Based on the information below, is RST~ABC? Explain. RS = x2 + 4x - 21, RT = x2 + 5x - 24, ST = x2 + 9x - 36 AB = x + 7, AC = x + 8, BC = x + 9

No, the corresponding sides are not proportional.

Analyze the diagram below and complete the instructions that follow. Based on the diagram above, a student determined the hypotenuse of the triangle to be 6√3. Determine if the student's answer is correct. If it is not correct, find the correct length.

No, the hypotenuse should be 12

The ratio of the measure of an exterior angle of a triangle to the measure of the adjacent interior angle is 1:4. Is the triangle acute or obtuse? Justify your answer.

Obtuse; the measure of the interior angle must be 144°.

Analyze the diagram below and complete the instructions that follow. Complete the proportion based on the similar triangles in the diagram.

QR

Which statement about kite PQRS must be true?

RP | QS

Analyze the diagram below and complete the instructions that follow. The perimeter of RXA is 39. If PX=4 and AP=9, find RX and RA.

RX=8, RA=18

Analyze the diagram below and answer the question that follows. In the portion of the shuffleboard court shown above, RS/QS = RT/QU. What additional piece of information do you need to show that RST~QSU using the SAS similarity theorem?

SRT = SQU

Which of the following is not a property of quadrilaterals?

There are four diagonals.

If a, b and c are all positive integers in a right triangle, they form a Pythagorean triple.

True

Analyze the diagram below and answer the question that follows. Are the two smaller triangles similar? If so, write the similarity statement and identify which theorem or postulate is used to prove the two triangles similar.

Yes, ABC~CBD by the SAS similarity theorem.

Analyze the diagram below and complete the instructions that follow. Are the polygons shown here similar? Justify your answer. The images are not drawn to scale.

Yes, PQR ~TSV with a scale factor of 1:√3

Determine if a triangle with the given dimensions is a right triangle. If it is, which angle is the right angle? AB=5 √3, BC= 10, CA=5

Yes, angle A is the right angle.

Analyze the diagram below and complete the instructions that follow. Determine whether KM//JN. Explain.

Yes, because 16/10 = 24/15

Can a triangle have an angle that measures /? If so, what type of triangle would it be?

Yes, such a triangle would be obtuse.

Determine if the segment lengths form a triangle. If so, would the triangle be acute, right, or obtuse? 24,30,6,√43

Yes, the segments would form an obtuse triangle.

Determine if the segment lengths form a triangle. If so, would the triangle be acute, right, or obtuse? 4.1, 8.2, 12.2

Yes, they would form an obtuse triangle.

Analyze the diagram below and complete the instructions that follow. Find a, b, and c.

a= 4√6 b=8√2 c= 4√2

If a, b, c, and d are four different numbers and the proportion a/b = c/d is true, which of the following is false?

b/a = c/d

ABCD is a parallelogram. If m<D increases, then m<C__.

decreases

Analyze the diagram below and complete the instructions that follow. Determine if the proportion e/d = d/f is true. If it is not true, correct the error.

false, it should be e/d = d/g

A quadrilateral has two consecutive angles that measure 90° each. Which of the following quadrilaterals could have this property? i. square ii. rectangle iii. parallelogram iv. kite v. rhombus vi. trapezoid

i, ii, iii, v, vi

If a quadrilateral is a parallelogram, then __________.

its consecutive angles are supplementary

Analyze the diagram below and complete the instructions that follow. In the figure, AB//CD. If the ratio of the perimeter of CEDto that of BEA is 3:2 and the sum of the perimeters of the two triangles is 110, find the perimeter of each triangle.

perimeter of CED = 66 perimeter of BEA = 44

Analyze the diagram below and complete the instructions that follow. In the figure, AB//CD. If the ratio of the perimeter of BEA to that of CED is 3:5 and the sum of the perimeters is 320, find the perimeter of each triangle.

perimeter of CED=200 perimeter of BEA=120

A kite has __________.

perpendicular diagonals

A kite is a __________.

quadrilateral

Give the most accurate name for this figure.

quadrilateral

Analyze the diagram below and complete the instructions that follow. Find the sine and the cosine of 30

sin 30 = 1/2, cos 3o = √3/2

All __________ are similar.

squares

Analyze the diagram below and complete the instructions that follow. Given that BC//DE//FG, find the value of each variable.

w = 6, x = 3, y = 1, z = 9

OQ is a diagonal of quadrilateral NOPQ. If m<NOQ=(9y-47), m<PQO= (y+73), NO = 5x + 12, and PQ = 7x - 8, find the values of x and y that make NOPQ a parallelogram.

x = 10, y = 15

Given that ABCD is an isosceles trapezoid, find x and y.

x = 15, y= 40

Given that DEFG is a square, find x and y.

x = 7, y = 9

Analyze the diagram below and complete the instructions that follow. Solve for x and y.

x = 7.5, y = 12.5

Quadrilateral JKLM has side lengths of JK = 3y + 4, KL = 8x - 12, LM = 5y - 6, and JM = 4x + 20. Find the values of x and y that make quadrilateral JKLM a parallelogram.

x = 8, y = 5

Find a possible solution to the equation sin(3x+13)= cos(4x)

x= 11

Analyze the diagram below and complete the instructions that follow. Find the value of x and the value of y.

x= 16, y= 9√2

Find a possible solution to the equation cos(x+2) = sin(3x)

x= 22