Geometry 2017 REQUIRES MATH

√a²+b²

(not a duplicate) What is the length of the hypotenuse of the triangle below? A)√a²+b² B) (2a+2b) C) (a²+b²) D) Not enough information is given.

(0,0)

A line segment has a midpoint of (-3, 2) and an endpoint of (-6, 4). What is the other endpoint of the line segment? A) (-9,6) B) (-4.5,3) C) (0,0) D) (9,2)

(10,7)

A line segment has a midpoint of (6, 4) and an endpoint of (2, 1). What is the other endpoint of the line segment? A) (-2,-2) B) (4,5) C) (7,10) D) (10,7)

50 meters

A man who is 2 meters tall is facing a tower that is 13 meters away. He can see the reflection of the top of the tower in a puddle that is 0.5 meter in front of him. What is the approximate height of the tower in meters?

80 m

A midsegment of a triangle measures 40 m. What is the length of the corresponding base of the triangle? A) 20 m B) 40 m C) 60 m D) 80 m

135 ft

A surveyor needs to measure the straight-line distance across a river and sets out stakes making two triangles, as shown below. Using similarity and the measures of the smaller triangle, how wide is the river in feet?

6/1

A total of 132 potential customers visit 22 vendors at a flea market. What is the ratio of customers to vendors? A) 1:6 B) 6/1 C) 22:132 D) 22/132

100 ft

A woman who is 6-ft tall casts a 4.5-foot shadow at the same time that a building casts a 75-foot shadow. What is the height of the building in feet?

70

For what value of x is the following quadrilateral a parallelogram? A) 30 B) 45 C) 60 D) 70

4

For what value of x is the following quadrilateral a parallelogram? A) 4 B) 5 C) 6 D) 8

9

For what value of x is the following quadrilateral a parallelogram? A) 5 B) 6 C) 9 D) 10

a = 12; b = 6

For what values of a and b is the following quadrilateral a parallelogram? A) a = 6; b = 12 B) a = 6; b = 2 C) a = 12; b = 6 D) a = 4; b = 8

6

There are 24 offices in a building that contains 4 floors. On average, how many offices are on each floor?

15:1

There are 45 boats on 3 docks. What is the ratio of boats to docks? A) 1/15 B) 3 to 15 C) 3:45 D) 15:1

(5, 3)

What are the coordinates of the undefined vertex in the parallelogram below? A) (1, 5) B) (3, 5) C) (4, 3) D) (5, 3)

3.1

If ∆ABC ~ ∆DEF, what is the length of EF to the nearest tenth? A) 2.5 B) 2.9 C) 3.1 D) 3.5

24°

If ∆ABC≅∆DEF, what is the measure of ∠F? A) 78° B) 24° C) 36° D) 42°

6 cm

If ∆ABC≅∆DEF,what is the length of line segment DF? A) 4 cm B) 6 cm C) 8 cm D) 10 cm

√2

What is the distance from the origin to the midpoint of the line segment defined by the endpoints (-4,0) and (2,-2)? A) √2 B) 2 C) √5 D) 2√10

22.5 in.

What is the length of AD in the following figure? A) 20.5 in. B) 22.5 in. C) 25.5 in. D) 27.5 in.

2√5

What is the length of the hypotenuse of the right triangle defined by the points (4, 2), (8, 2), and (8, 4)? A) 4 B)2√5 C)2√3 D)6

4√5

What is the length of the hypotenuse of the triangle below? A) 4√5 B) 12 C) 80 D) 4√3

-1

What is the slope of the line that contains the origin and the point (3, -3)? A) 0 B) 1 C) -1 D) The slope is undefined.

0

What is the slope of the line that contains the points (-6, -2) and (3, -2)? A) -³/₄ B) 0 C) ⁴/₉ D) The slope is undefined.

-⁴/₅

What is the slope of the line that contains the points (-6, 3) and (4, -5)? A) -4 B) ⁵/₄ C) -⁴/₅ D) ⁴/₅

⁹/₄

What is the slope of the line that contains the points (0, -8) and (4, 1)? A) ⁴/₉ B) ⁹/₄ C) 4 D) -⁷/₄

1

What is the slope of the line that contains the points (3, 4) and (1, 2)? A) 1 B) -1 C) ½ D) ³/₂

- ²/₃

What is the slope of the line that contains the points (4, -4) and (7, -6)? A) ³/₂ B) - ²/₃ C) - ³/₂ D) 2

The slope is undefined.

What is the slope of the line that contains the points (5, -9) and (5, 9)? A) 0 B) ⁵/₉ C) - ⁹/₅ D) The slope is undefined.

The slope is undefined.

What is the slope of the line that contains the points (8, 3) and (8, -7)? A) -4 B) -¼ C) 0 D) The slope is undefined.

The slope is undefined.

What is the slope of this line? A) 0 B) 2 C) -2 D) The slope is undefined.

0

What is the slope of this line? A) 1 B) 0 C) 3 D) The slope is undefined.

-1

What is the slope of this line? A) 1 B) 3 C) -1 D) -3

1

What is the slope of this line? A) 1/3 B) ½ C) 1 D) 2

-¹/₆

What is the slope of this line? A) 4 B) -³/₂ C) -¹/₆ D) The slope is undefined.

-²/₅

What is the slope of this line? A) ⁵/₂ B) 2 C) -²/₅ D) The slope is undefined.

-3

What is the slope of this line? A) -3 B) 3 C) ¹/₃ D) - ¹/₃

The slope is undefined.

What is the slope of this line? A) -4 B) 0 C) 1 D) The slope is undefined.

0

What is the slope of this line? A) -4 B) 0 C) ¼ D) The slope is undefined.

²/₃

What is the slope of this line? A) ²/₃ B) ³/₂ C) 2 D) The slope is undefined.

4

What is the value of x in the figure below? A) 4 B) 5 C) 9 D) 12

20

What is the value of x? A) 80 B) 20 C) 13.3 D) 10

76

What is the value of x? A) 18 B) 76 C) 162 D) 180

y = ²/₇ x +1

Which choice is the equation of a line that passes through point (7, 3) and is parallel to the line represented by this equation? y = ²/₇ x -3 A) 7x + 3y = 2 B) y = ²/₇ x +1 C) y = - ⁷/₂ x -3 D) 2x + 7y = 1

142°

In the figure below, m∠1 = 38°, what is m∠2? A) 38° B) 52° C) 90° D) 142°

4x− y = 0

Which choice is the equation of a line that passes through the origin and is parallel to the line represented by this equation? 4x− y = −8 A) 8x− y = −4 B) 4x− 8y = 0 C) y = −4x D) 4x− y = 0

2x + 5y = 36

Which choice is the equation of a line that passes through the point (-2, 8) and is perpendicular to the line represented by this equation? 5x − 2y = −10 A) 2x− 5y = 26 B) 5x + 2y = 10 C) 2x + 5y = 36 D) −2x + 5y = −13

y=¹/₃x

Which choice is the equation of a line that passes through the point (-6, -2) and is perpendicular to the line represented by this equation? y = −3x + 1 A) 3x + y = 1 B) y=¹/₃x C) y = −3x D) −3y = −x + 1

y = ⁵/₄ x -15

Which choice is the equation of a line that passes through the point (0, -15) and is parallel to the line represented by this equation? 5x− 4y = 12 A) y = ⁴/₅ x-8 B) y = ⁵/₄ x -15 C) y = - ⁵/₄ x +7 D) y = - ⁴/₅ x-12

y = x− 6

Which choice is the equation of a line that passes through the point (5, -1) and is perpendicular to the line represented by this equation? y = −x + 5 A) y = x− 6 B) 5x − y = 5 C) y = −x− 1 D) 2x− 5y = −1

A

Which choice is the graph of a line parallel to the line represented by this equation? y=²/₃x+2

C)

Which choice is the graph of a line that is perpendicular to the line represented by this equation? y = 3

C)

Which choice is the graph of a line that is perpendicular to the line represented by this equation? y = −2x + 7

10.5 in.

The base of a triangle measures 21 in. What is the measure of the corresponding midsegment of the triangle? A) 7 in. B) 10.5 in. C) 21 in. D) 42 in.

30 m

AD, BE, and CF are medians of ∆ABC. Given that AG = 20 m, find AD. A) 25 m B) 30 m C) 35 m D) 40 m

6 m

AD, BE, and CF are medians of ∆ABC. Given the lengths of CG and GF, what is the length of CF? A) 3 m B) 6 m C) 9 m D) 12 m

18 m

AD, BE, and CF are medians of ∆ABC. Given that AG =12 m, find AD. A) 18 m B) 20 m C) 22 m D) 24 m

18 in.

AD, BE, and CF are medians of ∆ABC. Given that CG = 36 in., find GF. A) 9 in. B) 12 in. C) 18 in. D) 24 in.

5 in.

AD, BE, and CF are medians of ∆ABC. Given the measurements of EG and GB, what is the length of EG? A) 3 in. B) 4 in. C) 5 in. D) 10 in.

5 ft

ED is a midsegment of ∆ABC . What is the length of DB? A) 5 ft B) 6 ft C) 8 ft D) 10 ft

10 in.

ED is a midsegment of ∆ABC. If ∆ABC is equilateral, what is the length of AD? A) 6 in. B) 8 in. C) 10 in. D) 12 in.

12 cm

ED is a midsegment of ∆ABC. What is the length of BC? A) 10 cm B) 12 cm C) 14 cm D) 18 cm

8

FD is a midsegment of ∆ABC. What is the length of BC? A) 3 B) 4 C) 6 D) 8

(-2,2)

Find the midpoint of a segment whose endpoints are (-9,5) and (5,-1). A) (-4,2) B) (-2,2) C) (2,-2) D) (4,-4)

(1,9)

Find the midpoint of a segment whose endpoints are (5,8) and (-3,10). A) (1,9) B) (9,1) C) (2,18) D) (8,-2)

7

Find the distance between the points (-4,6) and (3,6). A) 1 B) 7 C) 12 D) 49

10

Find the distance between the points (2,2) and (8,-6). A) 3 B) 7 C) 10 D) 12

2√122

Find the length of a segment with an endpoint of (-3, 1) and a midpoint of (8, 2). A)√26 B) 2√26 C) √122 D) 2√122

10

Find the length of a segment with an endpoint of (2, 5) and a midpoint of (5, 9). A) 3√2 B) 5 C) 7 D) 10

6.0

Given that AB = 6, BD = 2.4, and BC = 10, what is DE? A) 3.6 B) 4.0 C) 6.0 D) 6.7

√3

Given that AC = 1 and BC = 2, what is AB? A) √3 B) 3 C) 5 D) 2√2

51°

Given that m∠ABD = 97°, find m∠CBD. A) 44° B) 51° C) 92° D) 136°

69°

Given that m∠RST=111° and ∠XYZ is supplementary to ∠RST what is m ∠XYZ? A) 69° B) 48° C) 42° D) 21°

6

If (2, 5) and (x, 6) are the endpoints of a segment with length √17, what is the value of x? A) 2 B) 5 C) 6 D) 8

BC < CD

If m∠BAC = (5x - 2)° and m∠CAD = (6x+4)°, what can we conclude from the figure below? A) BC < CD B) BC ≥ CD C) CD < BC D) CD ≅ BC

5 m

MN is a midsegment of ∆JKL. What is the length of MN ? A) 4 m B) 5 m C) 6 m D) 8 m

20 birdies

Susan averages 8 birdies in an 18-hole round of golf. How many birdies should she expect after playing 45 holes?

The slope of the hypotenuse is negative.

The coordinates of the vertices of a right triangle are (-2,-2), (7,-2), and (7,4). Which of the following statements is false? A) One leg lies below the x-axis. B) The origin lies outside of the triangle. C) The length of the hypotenuse is greater than 9. D) The slope of the hypotenuse is negative.

(7, 12)

The height of this isosceles triangle is twice the length of its base. What are the coordinates of the undefined vertex? A) (7, 6) B) (6, 7) C) (7, 12) D) (12, 7)

(1,1)

WXYZ is a rectangle. At which point do the diagonals intersect? A) (-1,-1) B) (1,1) C) (0,0) D) (2,1)

(8, 2) and (2, 2)

What are endpoints of a line segment that divides the triangle defined by the vertices (2, 2), (8, 0), and (8, 4) into two congruent triangles? A) (5, 1) and (8, 4) B) (5, 3) and (5, 1) C) (8, 2) and (2, 2) D) (8, 0) and (5, 3)

y=³/₂x+4

Which choice could be the equation of a line parallel to the line represented by this equation? 3x− 2y = 6 A) 2x− 3y = 6 B) y=³/₂x+4 C) 5x− y = −2 D) y=²/₃x-8

y= 2x + 7

Which choice could be the equation of a line parallel to the line represented by this equation? y = 2x− 3 A) y=-½x+4 B) y= 2x + 7 C) y = −2x + 1 D) y=³/₂x-5

y = ⁷/₁₂ x -9

Which choice could be the equation of a line parallel to the line represented by this equation? 7x− 12y = −32 A) y = ₁₂/₇ x-3 B) y = - ⁷/₁₂ x +5 C) y = ⁷/₁₂ x -9 D) y = 7x− 12

y=⁷/₄x+11

Which choice could be the equation of a line parallel to the line represented by this equation? y=⁷/₄x-6 A) y=⁴/₇x-3 B) y=-⁴/₇x-6 C) y=⁷/₄x+11 D) 4x− 7y = −7

y=-¼x+3

Which choice could be the equation of a line perpendicular to the line represented by this equation? 4x− y = −8 A) y− 4x = −8 B) x− 4y = 8 C) y=−4x + 2 D) y=-¼x+3

x = 5

Which choice could be the equation of a line perpendicular to the line represented by this equation? y = 5 A) y = 4x− 9 B) y = - ¹/₅ x C) y = 5x D) x = 5

y = - ¹/₅ x+5

Which choice could be the equation of a line perpendicular to the line represented by this equation? y = 5x− 2 A) y = - ¹/₅ x+5 B) y = 5x +2 C) y = ¹/₅ x-7 D) y = −5x + 5

y = - ⁵/₂ x -3

Which choice could be the equation of a line perpendicular to the line represented by this equation? y = ²/₅ x +2 A) y = ²/₅ x -3 B) y = ⁵/₂ x +7 C) y = - ⁵/₂ x -3 D) y = −2x + 5

y = - ³/₂ x -3

Which choice is the equation of a line that has a y-intercept of -3 and is perpendicular to the line represented by this equation? y = ²/₃ x + 1 A) y = ²/₃ x-3 B) y = 3x− 3 C) y = - ³/₂ x -3 D) y = ³/₂ x +3

y = 6x+ 7

Which choice is the equation of a line that has a y-intercept of 7 and is parallel to the line represented by this equation? y = 6x− 5 A) y = 6x+ 7 B) y = 6x− 7 C) y=-¹/₆x+7 D) y=¹/₆x-7

y=⁵/₃x-18

Which choice is the equation of a line that passes through (9, -3) and is parallel to the line represented by this equation? y=⁵/₃x-4 A)y=⁵/₃x-18 B) y=⁵/₃x+4 C) y=-³/₅x-5 D) y = 5x− 4

2, 5, 4

Which set of numbers could be the lengths of the sides of a triangle? A) 2, 5, 4 B) 3, 5, 9 C) 4, 9, 3 D) 17, 15, 2

15, 8, 9

Which set of numbers could be the lengths of the sides of a triangle? A) 4, 9, 5 B) 2, 4, 6 C) 8, 3, 2 D) 15, 8, 9

35

∆ABC≅∆DEF by ASA. What is the value of x? A) 70 B) 40 C) 35 D) 110

x = 5 and y = 2

∆DEF≅∆LMN. What are the values of x and y? A) x = 3 and y = 5 B) x = 4 and y = 6 C) x = 5 and y = 2 D) x = 6 and y = 3

15 mm

∆XYZ≅∆PQR. What is the length of line segment PQ? A) 12 mm B) 15 mm C) 8 mm D) 20 mm

70°

∆XYZ≅∆PQR. What is the measure of ∠Y? A) 80° B) 30° C) 70° D) 100°