Geometry Final Review

Round to the nearest tenth.

A = 18 degrees a = 3.4 b = 10.5

Jan is constructing an inscribed circle in a triangle. What is the center of this circle called?

incenter

If point (x, y) is rotated 270 degrees about the origin, the resulting point is (y, -x).

True

Ralph bought a dozen widgets and it cost $30. How much will 80 widgets cost?

$200

A triangle has vertices of (0,3.5), (3,1.5), (0, -1.5). If it is dilated with center at the origin, and a scale factor of 2, what will be the coordinates of the image?

(0,7), (6,3), (0, -3)

Solve for x. Round to the nearest hundredth. tan 51 degree= x/14.8

18.28

Under the translation \left( {x + 1,\;y - 5} \right)(x+1,y−5) the point (-1, -4) will become (0, -9)

True

The table below shows a set of points forming figure ABCD. Complete the table for the indicated dilation rule.

(x, y)(5x, 5y)A (2, -1)A' (10, -5)B (0, -5)B' (0, -25)C (-3, 1)C' (-15, 5)D (1, -2)D' (5, -10)

John left a scavenger hunt for his friends! He advised his friends to travel 5 blocks west and 3 blocks north. Which translation rule below describes John's instructions? Correct answer: \left( {x,\;y} \right)\; \to \;\;\left( {x - 5,\;y + 3} \right)

(x,y)- (x-5, y+3)

The cosine of 63 degrees is 0.45. What is the sine of 27 degrees?

0.45

The cosine of 50 degrees is 0.64. What is the sine of 40 degrees?

0.64

The sine of 72 degrees is 0.95. What's the cosine of 18 degrees?

0.95

Molly is designing a new drone for the Air Force. The drone is supposed to be 30 feet long and 4 feet tall. She is building a prototype for testing that will be 12 feet long. How tall should the prototype be?

1.6 feet

The distance from B to B' is 6 and the distance from A to B' is 2. What is the scale factor?

1/4

The distance from A to B is 10 and the distance from A to B' is 2. What is the scale factor?

1/5

Find the Value of y.

10

Megan bikes 6 miles west to get from her apartment to school. After school, she bikes 8 miles north to her friend Izaac's house. How far is Megan's apartment from Izaac's house, measured in a straight line?

10 miles

The park is 6 miles due west of your house, and the library is 11 miles north of your house. How far is the shortest distance from the park to the library? Round to the nearest half mile.

12.5 miles

A dog has dug holes in diagonally-opposite corners of a rectangular yard. One length of the yard is 8 meters and the distance between the two holes is 17 meters. How wide is the yard?

15 meters

What is the measure of arc RT?

156 degrees

A candy bar sells for 4 for $5. How many can be bought for 20 dollars?

16 bars

A park ranger is looking out from their station at a 30 degree angle of depression. The ranger is 80 feet above the ground. How far is it from the ranger up in the station down to the fire? Round to the nearest hundredth.

160 feet

Standing on one bank of a river, an explorer measures the angle to the top of a tree on the opposite bank to be 27 degrees. He backs up 50 feet and measures the angle to the top of the tree to now be 22 degrees. How wide is the river? Round to the nearest tenth of a foot.

191.5 feet

If the distance from C to C' is 8 and the scale factor is 5. What is the distance from A to C?

2

What is the measure of arc RST?

204 degrees

David is trying to solve the following. If 24 people have the flu out of 360 people, how many would have the flu out of 900? Choose EVERY proportion that David could use to solve this problem.

24/360=x/900 900/360=x/24

If the measure of arc AB is 50 degrees, what is the measure of angle ADB?

25 degrees

Solve for x. Round to the nearest tenth of a degree.

26.6 degrees

△ABC has been rotated __________ counter-clockwise around the origin.

270 degrees

Find the Value of x.

28

If the distance from D to D' is 10 and the distance from A to D is 5, what is the scale factor?

3

What is the scale factor of the dilation?

3

A quality control technician checked a sample of 30 bulbs. Two of the bulbs were defective. If the sample was representative, find the number of bulbs expected to be defective in a case of 450.

30

Find the distance "x" across the river.

30

The measure of arc XY is 85 degrees. The measure of arc WZ is 25 degrees. What is the measure of angle 3?

30 degrees

What is the value of x.

35

What is the length of segment AD?

4.5

Which proportion can be used to find the value of y?

4/8= y/14

Solve for x. Round to the nearest tenth if necessary.

41.1

Solve for Z. Round to the nearest hundredth.

47.66

In a 30-60-90 triangle, the hypotenuse has a length of 10. How long is the shorter leg (across from the 30 degree angle)?

5

Segments AB and BC are both tangent to the circle shown above. What is the length of BC? *Note: photo not necessarily to scale

5

Given a 45-45-90 triangle with a leg length of 5, what is the length of the hypotenuse?

5 underroot 2

Solve for x.

5.34

If there are 15 girls and 9 boys in an art class, the ratio of girls to boys in the class is _______.

5/3

Find the value of z.

50/3

If \bigtriangleup ABC\sim\bigtriangleup DEF△ABC∼△DEF, find m∠A.

54 degree

A flagpole stands in the middle of a flat, level field. 50 feet away from its base, a surveyor measures the angle to the top of the flagpole as 48 degrees. How tall is the flagpole? Round to the nearest hundredth of a foot.

55.53 feet

Find the value of x.

6 2/3

Given a 30-60-90 triangle whose shortest leg is 3 centimeters, what is the length of the hypotenuse?

6 cm

What is the cosine of angle B?

7 underroot 65/65

This fall, 126 students participated in the soccer program, while 54 played volleyball. What was the ratio of soccer players to volleyball players

7/3

The measure of arc PQR is equal to 250 degrees. The measure of arc PR is equal to 110 degrees. What is the measure of angle 2?

70 degrees

The bottom of a slide at the playground is 6 feet from the base of the play set. The length of the slide is 10 feet. How tall is the slide?

8 feet

If c = 16, solve for b.

8 underroot 3

A meteorologist measures the angle of elevation to her weather balloon as 33 degrees. A radio signal from the balloon indicates that it is 1601 meters diagonally from her location. How high is the weather balloon above the ground? Round to the nearest hundredth.

871.97 feet

Paige is in a hot air balloon that has just taken off and is floating above its launching point. Ryan is standing on the ground, 12 meters away from the launching point. If Paige and Ryan are 15 meters apart, how high up is Paige?

9 meters

Which proportion could be used to find the value of v.

9/6= 8/v

Line l is tangent to circle Q. What is the measure of the angle formed at the point of tangency?

90 degrees

A baseball "diamond" is actually a square with side lengths of 90 feet. In a game, a runner tries to steal second base. How far must the catcher throw from home plate to second base in order to get the runner out?

90 underroot 2 feet

Choose EVERY true proportion.

AB/AD = AC/CE AB/AD= BC/DE AC/AE= BC/DE

Which of the following require that you have parallel sides?

Alternate Interior Angles

Which angle is congruent to angle P?

Angle B

Which angle is congruent to angle B?

Angle F

f point (x, y) is rotated 180 degrees about the origin, the resulting point is (-x, -y).

True

If chord AB is congruent to chord CD, then what must be true about EF and EG?

They are the same length

If point (x, y) is rotated 90 degrees about the origin, the resulting point is (-y, -x).

False

Under the translation \left( {x - 2,\;y + 3} \right)(x−2,y+3) the point (0, -4) will become (-2, -7)

False

When an object is reflected over a line, the resulting image is not congruent to the original image.

False

If the pentagon below is to be reflected over the line y=x, what are the new coordinates of the vertices?

G' (4, 0) H' (3, 2) J' (-2, 2) K' (-2, -2) L' (3, -2)

A sign is being created using two trapezoids where trapezoid E'F'G'H'EFGHE′F′G′H′EFGH . The table of translations is below.

H' (0, -1)

A company produces metal slabs for industrial use. The slabs come in 3 thicknesses: 5in, 10in, and 15in. The weights of each thickness for each metal are given below. Metal 1: 150lbs, 300lbs, 600lbs Metal 2: 130lbs, 260lbs, 390lbs Metal 3: 310lbs, 620lbs, 930lbs Metal 4: 140lbs, 280lbs, 420lbs For which of the metals is weight NOT proportional to thickness?

Metal 1

Choose the theorem below that can NOT help you determine the measure of an angle.

MidPoint

If the pentagon below is to be reflected over the y-axis, which point would not move at all?

Point G

Which point is a reflection of point K over the x-axis?

Point L

Given any two side lengths in a right triangle, what is used to find the third side length?

Pythagorean Theorem

Which of the following can be used when two triangles share an angle?

Reflexive

Which side is the "adjacent" side to θ?

a

If c = 6, solve for a.

a= 3 underroot 2

Inverse cosine is used to find a given angle measure when we know the ________ and the ________.

adjacent side; hypotenuse

Which of the following constructions must you know how to do in order to construct an inscribed circle for a given triangle?

angle bisector

The city of Covington is placing a statue in a triangular grassy area bounded by sidewalks on all 3 sides. If the city wants the statue to be an equal distance from all 3 sides of the grassy area, where should they place it? Correct answer:

at the incenter of the triangle

Kim is constructing the circumscribed circle about a triangle she drew. What is the center of this circle called?

circumcenter

Nate is constructing a tangent line to a circle he drew from a point outside the circle. Once he has the circle and the point drawn, what is his next step?

connect the center of the circle to the point outside the circle

Kris has 3 daughters who all live in different cities across Georgia. She wants to live somewhere that is an equal distance from each of her daughters. She mapped out the 3 cities and drew a triangle connecting them. How can she find a point on the map that is an equal distance from all 3 cities?

construct the circumcenter

A quadrilateral inscribed in a circle is called a _________________.

cyclic quadrilateral

The angle of elevation from object A to object B is always ______ the angle of depression from object B to object A.

equal to

What inverse trig function would be used to solve for angle Z?

inverse sine

Inverse tangent is used to find a missing angle measure when we are given the ________ and the _________

opposite side; adjacent side

Inverse sine is used to find a given angle measure when we know the _________ and the __________.

opposite side; hypotenuse

Which of the following constructions must you know how to do in order to construct a circumscribed circle for a given triangle?

perpendicular bisector

Which of the following is NOT used in geometric constructions?

protractor

What inverse trig function can be used to find the measure of angle A?

sin−1

Which of the following is NOT true of a perpendicular bisector?

to construct it, we have to draw two arcs using the intersection points as centers

When an object is rotated around a point, the resulting image is congruent to the original pre-image.

true

△GHK has been reflected over what line to create the resulting image?

x-axis

Solve for x.

x=15

The pentagon shown could be reflected over which line to be carried onto itself?

y-axis

△GHK has been reflected over what line to create the resulting image?

y-axis

Solve for y.

y=5