Geometry Semester test

The zoom feature on a camera lens allows you dilate what appears on the display. When you change from 100% to 500%, the new image on your screen is an enlargement of the previous image with a scale factor of 5. If the new image is 47.5 millimeters wide, what was the width of the previous image?

A (9.5 millimeters)

In trapezoid PQRS, PQ A SR. Find the area of PQRS. Leave your answer in simplest radical form.

A (144+ 72squareroot 3 units^2)

Find the area. The figure is not drawn to scale. (rectangle w/ triangle, numbers included- 9cm, 8cm, 13cm, 11cm)

A (144.5 cm2)

Sears tower

A (1:725)

Find the area. The figure is not drawn to scale. (sides- 7.6cm, 3.7 cm)

A (28.12 cm2)

What is the value of x? (sides- x, x-2, x+1, x+5)

A (5)

What is the value of x, given that AE A BD?

A (7 6/7)

ABCDE~GHJDF. Complete the statements. A.<H congruent to ___ B. GH/DJ=AB/__

A (<B; DC)

Find the length of the missing side. The triangle is not drawn to scale. (sides-17 and 15)

A (8)

Use the information in the diagram to determine the height of the tree to the nearest foot.

A (80ft)

Are the two triangles similar? How do you know? (two triangles together ABD and CBD)

A (ADB~CDB; SAS~)

What similarity statement can you write relating the three triangles in the diagram? (the letters are M,J,K,L)

A (JMK~MLK~JLM)

Write a sequence of rigid motions that maps RST to DEF.

A (Rst U r (270,p))(RST)=(DEF)

Name the translation image of ABC equivalent to (Rr OR, ABC).

A (UVW)

What similarity statement can you write relating the three triangles in the diagram? (the letters are V,T,U,W)

A (UVW~UWT~WVI)

What are the values of a and b? (sides-b, 10, 8, a, 6)

A (a= 9/2, b= 15/2)

Find the length of the missing side. Leave your answer in simplest radical form. (sides- 13ft, 10ft)

A (square root 69ft)

Write the tangent ratios for <Y and <Z.

A (tanY= 7/4, tanZ= 4/7)

Find the value of w and then x. Round lengths to the nearest tenth and angle measures to the nearest degree. (sides- 10, 11 angles-x, 50)

A (w = 7.7, x = 44)

What is value of x, given that OP A NQ?

A (x=10)

The polygons are similar, but not necessarily drawn to scale. Find the value of x. Sides of first triangle: x-3, 8, 16

A (x=13)

Which graph shows T<-4,2> (ABC)?

A

The glide reflection Ry=-x OT<4,1> maps the point P to (4, 3). Find the coordinates of P.

A (-2,0)

n-6/3n=n-5/3n+1

A (-3)

Find the area. The figure is not drawn to scale. (sides- 36in, 40in. height-33in)

A (1188 in2)

What is the value of x, given that PQ A BC?

A (12)

The vertices of a triangle are P(-8, 6), Q(1, -3), and R(-6, -3). Name the vertices of Ry=x (PQR)

B ( P'(6,-8), Q'(-3,1), R'(-3,-6))

A carnival ride is drawn on a coordinate plane so that the first car is located at the point (30,0). What are the coordinates of the first car after a rotation of 270° about the origin?

B (0,-30)

The dashed triangle is a dilation image of the solid triangle. What is the scale factor?

B (1/2)

Two rectangles 4m by 12m and 8m by 24m

B (12/4=24/8)

A grid shows the positions of a subway stop and your house. The subway stop is located at (-7, 8) and your house is located at (6, 4). What is the distance, to the nearest unit, between your house and the subway stop?

B (14)

Red and Grey bricks

B (160)

Find the area of the rhombus. (9m,9m,9m,9m)

B (162m^2)

Find the area. The figure is not drawn to scale. (numbers included- 8in, 11in, 9in.

B (278in2)

In FGH, g = 8 ft, h = 13 ft, and m<F= 72°. Find m<G. Round your answer to the nearest tenth.

B (35.9)

Use a trigonometric ratio to find the value of x. Round your answer to the nearest tenth. (sides- x, 4 angles-40)

B (4.8)

Quilt squares are cut on the diagonal to form triangular quilt pieces. The hypotenuse of the resulting triangles is 10 inches long. What is the side length of each piece?

B (5 square root 2)

Find the length of the hypotenuse. (angle-45, side- 3square root 2)

B (6)

Find the measure of a. (triangle ABC, sides-a, 8, 11. Angle- 32.2)

B (6)

Cos ___ =2/5

B (66.42)

Find the measure of AB given m<A= 55°, m<B= 44°, and b = 68.

B (96.68)

Find the image of C under the translation described by the translation rule T<4,5> (C)

B (E)

Are the two triangles similar? How do you know? (triangle QSR and VUT with angles 29, 29)

B (QRS~VTU; SAS~)

Write a rule in function notation to describe the transformation that is a reflection across the y-axis.

B (Rx=0 (x,y))

Name the image of FC,

B (ST)

Find the translation rule that describes the translation B to E.

B (T<0,15> (B))

Given the regular polygon, find the measure of each numbered angle. (1, 2)

B (m<1=45, m<2=67.5)

The dashed-lined figure is a dilation image of EFGH. Is D(n, H) an enlargement or a reduction? What is the scale factor n of the dilation?

B (n=3; enlargement)

Which type of isometry is the equivalent of two reflections across intersecting lines?

B (rotation)

Find the area of the rhombus. Leave your answer in simplest radical form. (60 degrees, 9)

C (162 square root 3 units^2)

On a baseball field, the pitcher's mound is 60.5 feet from home plate. During practice, a batter hits a ball 216 feet deep. The path of the ball makes a 34° angle with the line connecting the pitcher and the catcher, to the right of the pitcher's mound. An outfielder catches the ball and throws it to the pitcher. How far does the outfielder throw the ball?

C (169.3 ft)

Find the area of the trapezoid. Leave your answer in simplest radical form (sides- 19in, 14.5in, 29.2in, 12.6in)

C (303.66in^2)

What is the area of the kite? (6ft, 12ft, 2ft, 2ft)

C (36ft^2)

Find the image of P(-2, -1) after two reflections; first Ry=-5 (P), and then Rx=1 (P')

C (4,-9)

Given a regular octagon, find the measures of the angles formed by (a) two consecutive radii and (b) a radius and a side of the polygon.

C (45°; 67.5°)

Ratio length to width in a rectangle is 3 to 1

C (51 feet)

Plots of land between two roads are laid out according to the boundaries shown. The boundaries between the two roads are parallel. What is the length of Plot 3 along Cheshire Road?

C (53 1/3)

Find m<B given that c=83, a=44, and m<A=31

C (72.7)

4/a=16/32

C (8)

Find the value of x. Round the length to the nearest tenth. (sides- 12cm, x angles- 35)

C (8.4 cm)

Airplane with person and radar tower

C (<2 is the angle of elevation from the radar tower to the airplane.)

Which side has an equal measure to BC?

C (EF)

The hexagon GIKMPR and FJN are regular. The dashed line segments form 30° angles. What is r(240,0)(G)?

C (K)

Write the ratios for sin X and cos X.

C (SinX=squareroot 119/12, CosX=5/12)

Write a sequence of rigid motions that maps AB to XY

C (T<-1,0> Ur (90,p))(AB)=(XY)

Jessica was sitting in row 9, seat 3 at a soccer game when she discovered her ticket was for row 1, seat 1. Write a rule to describe the translation needed to put her in the proper seat.

C (T<-8,-2> (Jessica))

From the similar triangles in the diagram, write a proportion using the ratio WX/WV.

C (VX/VY=WV/WY)

Triangle ABC has side lengths 3, 4, and 5. Do the side lengths form a Pythagorean triple? Explain

C (Yes, they form a Pythagorean triple; 3^2+4^2=5^2 and 3, 4, and 5 are all nonzero whole numbers.)

Use the composition (Rl UR(-90,C'))(ABC)=DEF , shown below. Which angle has an equal measure to m<B?

C (m<F)

Find the lengths of the missing sides in the triangle. Write your answers as integers or as decimals rounded to the nearest tenth. (sides-8, y, x angle- 45)

C (x = 11.3, y = 8)

The polygons are similar, but not necessarily drawn to scale. Find the value of x. Sides of first triangle: 16, x-1, y+1, 32

C (x=9)

Are the two triangles similar? How do you know? Angles: 39, 39

C (yes, by AA~)

Find the glide reflection image of the black triangle for the composition (Rx=1 OT<0,-7>)

D

Each triangle in the diagram is a reflection of another triangle across one of the given lines. How can you describe Triangle 3 by using a reflection rule?

D ( Rl(Triangle 2)

Find the area of a regular hexagon with an apothem 17.3 miles long and a side 20 miles long. Round your answer to the nearest tenth.

D (1038 mi^2)

Find the length of the leg. If your answer is not an integer, leave it in simplest radical form. ( side- 24 angle-45)

D (12 square root 2)

To find the height of a pole, a surveyor moves 140 feet away from the base of the pole and then, with a transit 4 feet tall, measures the angle of elevation to the top of the pole to be 44. To the nearest foot, what is the height of the pole?

D (139 ft)

Find the value of x. Round to the nearest tenth. (sides- x, 12 angles- 32)

D (14.2)

Find the area. The figure is not drawn to scale. (h=3yds Length- 10yds)

D (15yd2)

81 and 4

D (18)

Find the area of a regular hexagon with side length of 10 m. Round your answer to the nearest tenth.

D (259.8 m^2)

A blueprint for a house has a scale factor n = 45. A wall in the blueprint is 9 in. What is the length of the actual wall?

D (33.75 feet)

Find the measure of b, given m<A= 38°, m<B= 74°, and a = 31.

D (48.4)

Find m<C to the nearest tenth if c=48, a=34 , and m<A=41.

D (67.9)

Find the value of x. Round the length to the nearest tenth. (sides- 16m, x angles- 22)

D (6m)

Find the area of the trapezoid. Leave your answer in simplest radical form (sides- 7in, 8in, 8in, 12in)

D (70in^2)

In JKL, j=12cm, k=9cm, and l=9.75cm. Find m<J.

D (79)

A microscope shows you an image of an object that is 140 times the object's actual size. So the scale factor of the enlargement is 140. An insect has a body length of 6 millimeters. What is the body length of the insect under the microscope?

D (840 millimeters)

Find m<C to the nearest tenth. (sides- 24, 38 angle-39)

D (85.2)

In the diagram, figure RQTS is the image of figure DEFC after a rigid motion. Name the image of <F.

D (<S)

Find r(120,0)(OL)

D (OH)

In the diagram, ABC congruent to LMN. What is a congruence transformation that maps ABC onto LMN?

D (Ry=-x UT<0,2>)(ABC)=(LMN)

Write a rule in function notation to describe the transformation that is a reflection across the x-axis.

D (Ry=0 (x,y))

What is a rule that describes the translation ABCD to A'B'C'D'?

D (T<-3,2> (ABCD))

Which angle has an equal measure to <C?

D (m<E)

Are the triangles similar? How do you know? Measures of first angle: 30.4, 84.6

D (no)

A triangle has sides of lengths 27, 79, and 84. Is it a right triangle? Explain.

D (no; 27^2+79^2=84^2)

Find the value of x and y rounded to the nearest tenth. (sides- x, 34, y angle-30, 45)

D (x = 24.0, y = 46.4)

Suppose you are given information about a triangle according to SSS, SAS, and ASA. For which of these can you immediately use the Law of Cosines to find one of the remaining measures?

D. (SSS and SAS)

In ΔQRS, QR = 4, RS = 15, and m∠R = 36. In ΔUVT, VT = 8, TU = 32, and m∠T = 36.

The triangles are not similar