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Geometry Midterm Review Packet

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Geometry: Midterm Multiple Choice Practice

1. In the diagram below, a square is graphed in the coordinate plane.

A reflection over which line does not carry the square onto itself?

(1) (2) (3) (4)

2. A sequence of transformations maps rectangle ABCD onto rectangle A"B"C"D", as shown in the diagram

below.

Which sequence of transformations maps ABCD onto A'B'C'D' and then maps A'B'C'D' onto A"B"C"D"?

1) a reflection followed by a rotation

2) a reflection followed by a translation

3) a translation followed by a rotation

4) a translation followed by a reflection

3. Which equation represents a line that is perpendicular to the line represented by ?

(1) (2) (3) (4)

4. A line segment has endpoints A(7, −1) and B(−3, 3). What are the coordinates of the midpoint of AB?

(1) (1, 2) (2) (2,1) (3) (−5, 2) (4) (5, −2)

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5. What is the length, to the nearest tenth, of the line segment joining the points (4, 2) and (146, 52)?

(1) 141.4 (2) 150.5 (3) 151.9 (4) 158.1

6. What is the slope of the line that passes through the points (4, −7) and (9, 1)?

(1) 5

8 (2)

8

5 (3) −

6

12 (4) −

13

6

7. In the diagram below of , side is extended to point D, , , and .

What is ?

8. In , , , and . Which statement is true?

1) 2) 3) 4)

9. In the diagram of below, is drawn to side . If , , and , which type

of triangle is ?

(1) equilateral (2) scalene (3) obtuse (4) right

1) 5

2) 20

3) 25

4) 55

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10. In the diagram below, transversal intersects and at V and W, respectively.

If and , for which value of x is ?

(1) 6 (2) 16 (3) 24 (4) 28

11. Right triangle ABC is shown in the graph below. After a reflection over the y-axis, the image of is

. Which statement is not true?

(1) (2) (3) (4)

12. What are the coordinates of P′, the image of P(−4,0) under the translation (x − 3,y + 6)?

(1) (−7,6) (2) (7,−6) (3) (1,6) (4) (2,−3)

13. A translation moves P(3, 5) to P′(6, 1). What are the coordinates of the image of point (−3, −5) under the

same translation?

(1) (0, −9) (2) (−5, −3) (3) (−6, −1) (4) (−6, −9)

14. For a triangle, which two points of concurrence could be located outside the triangle?

(1) incenter and centroid

(2) centroid and orthocenter

(3) incenter and circumcenter

(4) circumcenter and orthocenter

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15. In the diagram of below, A is the midpoint of , B is the midpoint of , C is the midpoint of

and and are drawn. If and , what is the length of ?

(1) 5 (2) 13 (3) 16 (4) 32

16. As shown in the diagram below, bisects and .

Which method could be used to prove ?

(1) SSS (2) AAA (3) SAS (4) AAS

17. In the diagram below of and , , and .

To prove that and are congruent by SAS, what other information is needed?

1) 2) 3) 4)

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18. In shown below with , , , and , .. Which statement must be true?

(1) (2) (3) (4)

19. As shown in the diagram below of , a compass is used to find points D and E, equidistant from point

A. Next, the compass is used to find point F, equidistant from points D and E. Finally, a straightedge is used to

draw . Then, point G, the intersection of and side of , is labeled.

1) bisects side

3)

2) bisects

4)

20. Based on the construction below, which conclusion is not always true?

(1) (2) (3) (4)

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21. What is the midpoint of the line segment that joins points (4,2) and (2,5)?

(1) (1, 3

2) (2) (

3

2, 3) (3) (1,

7

2) (4) (2,

3

2)

22. What is the length of the line segment whose endpoints are and ?

(1) (2) (3) (4)

23. What is an equation of the line that passes through the point and has a slope of ?

24. What is an equation of the line that passes through the point and is parallel to the line whose equation

is ?

25. In the diagram of below, Jose found centroid P by constructing the three medians. He measured

and found it to be 6 inches.

If , which equation can be used to find x?

1) 2) 3) 4)

1)

2)

3)

4)

1)

2)

3)

4)

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Geometry: Midterm Short Answer Practice

1. Find the coordinates of point P along the directed line segment AB so that AP to PB is the given ratio.

A) A(1, 3), B(8, 4); 4 to 1 B) A(-2, 1), B(4, 5); 3 to 7

2. Determine if the following lines are parallel, perpendicular, or neither. Explain your reasoning.

A) 1

3 12 36 124

y x y x B) 4 2 4 2y x y x

5. Write equation of the line that passes through (-7, 5) and (0, 4).

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6. Point D is the centroid of triangle ABC. Use the given information to find the value of x.

5 3 2

4 1 6 4

AD x and DE x

DF x and BD x

7. Use a compass and straightedge to bisect angle C.

8. Use a compass and straightedge to construct a perpendicular bisector of AB.

A

B

C

A

B

C

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9. Use a compass and straightedge to construct an altitude drawn from B.

10. Find the measure of each acute angle in the right triangle.

A) the measure of one acute angle is 5 times the measure of the other acute angle.

B) The measure of one acute angle is 3 times the sum of the measure of the other acute angle and 8.

11. In ABC the measure of B is 4 more than three times the measure of A, and C is four times as large as A.

Find the measure, in degrees, of each angle in ABC .

12.

In the figure above, lines l and m are parallel, 55 100. .m a and m b Find m c

A

B

C

m

l

c

b

a

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13.

In the figure above, , 1 80. .PR RS and m Find m x

14.

In the figure above, find m d .

15.

x

1

S

R

P

35

d

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B

C

D E

A

16. In ,ABC D is a midpoint of BA and E is a midpoint of BC . If the measure of AC is 4 less than 3 times DE ,

what is the measure of DE ? (diagram is not drawn to scale)

17. Graph RSTU and MNOP on the coordinate plane below. Use appropriate scale to fit both figures. Determine whether

the polygons with given vertices are congruent or similar. Use the properties of rigid motions to explain your reasoning.

2, 3 , 2, 4 , 4, 6 , 0, 6 and 9, 1 , 9, 20 , 9, 10 , 3, 10R S T U M N O P

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Proofs:

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