Name ________________________ Midterm Review # 3Geometry Pd. _________ Date: _________

DIRECTIONS: Attempt all questions. YOU MUST SHOW ALL WORK TO EARN FULL CREDIT.

SECTION I

1. Given with base , median , altitude , and bisects , which conclusion is valid?

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

2. When writing a geometric proof, which angle relationship could be used alone to justify that two

angles are congruent?1) supplementary angles 3) adjacent angles2) linear pair of angles 4) vertical angles

3. What are the coordinates of , the image of , after a counterclockwise rotation of 90º about the origin?(1)(2)(3)(4)

4. How many sides does a polygon have if the sum of its interior angles is 720°?(1) 5 (2) 6(3) 7 (4) 8

5. Given that ABCD is a parallelogram, a student wrote the proof below to show that a pair of its opposite angles are congruent.

What is the reason justifying that ?1) Opposite angles in a quadrilateral are congruent.

2) Parallel lines have congruent corresponding angles.

3) Corresponding parts of congruent triangles are congruent.

4) Alternate interior angles in congruent triangles are congruent.

6. Side AB of parallelogram ABCD is represented by the equation y−7=32

x. Which equation could

represent sideCD?

(1) 2 y+14=3 x(2) 3 y−3=−2 x (3) 3 y+9=2 x

(4) y−5=23

x

7. In the diagram below, lines a and m are parallel with transversal t.  Find the number of degrees in the angle labeled x. 

8. If the vertices of are , , and , then is classified as1) right2) scalene3) isosceles4) equilateral

9. Which set cannot represent the lengths of the sides of a triangle?1)2)3)4)

10. In the diagram below, point P is the centroid of .

If and , what is the length of ?1) 92) 23) 184) 27

11. In the diagram of trapezoid ABCD below, diagonals and intersect at E and .

Which statement is true based on the given information?1)2)3)4)

12. If and is the shortest side of , what is the shortest side of ?

13.

14. In the diagram of below, is extended to point D.

If , , , what is ?1) 132) 253) 534) 65

1)2)3)4)

15. In the diagram below ofΔ ABC , mediansAD , BE , and CF intersect at G.

IfCF=24 , what is the length ofFG ?(1) 8(2) 10(3) 12(4) 16

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

Point P must be the1) centroid2) circumcenter3) incenter4) orthocenter

17. The vertices of the triangle in the diagram below are , , and .

What are the coordinates of the centroid of ?1)2)3)4)

18. In triangle ABC, m<A = 60 and m<B = 40. Which side of triangle ABC is the longest?

1) AC

2) AB

3) BC

4)BC ≅ AB

19. The slope of is and the slope of is . If , determine and state the value of x

Part IIAnswer all 4 questions in this part. Each correct answer will receive 2 credits. Clearly indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc. For all questions in this part, a correct numerical answer with no work shown will receive only 1 credit. All answers should be written in pen, except for graphs and drawings, which should be done in pencil. [8 points]

. Using a compass and straightedge, construct the perpendicular bisector of . [Leave all construction marks.]

20. Describe a sequence of rigid motions that will map Pentagon ABCD onto Pentagon A’’B’’C’’D’’

22. Complete the partial proof below for the accompanying diagram by providing reasons for steps 3, 6, 8, and 9.

Given: , , , ,

Prove:

Statements Reasons

1 1 Given

2 , 2 Given

3 and are right angles.

3

4 4 All right angles are congruent.

5 5 Given

6 6

7 7 Given

8 8

9 9

Part IIIAnswer all 2 questions in this part. Each correct answer will receive 4 credits. Clearly indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc. For all questions in this part, a correct numerical answer with no work shown will receive only 1 credit. All answers should be written in pen, except for graphs and drawings, which should be done in pencil. [8 points]

23a. Find the unknown angle in the diagram below:

23b. Explain how you solved for x.

Part IVAnswer the question in this part. A correct answer will receive 6 credits. Clearly indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc. A correct numerical answer with no work shown will receive only 1 credit. The answer should be written in pen. [6 points]

24.

Prove: ABCD is a Trapezoid but not an Isosceles Trapezoid. [The use of a grid is optional.]

25.

A)

B) The sides of Parallelogram MNPQ are represented by the expressions below. Sketch Parallelogram MNPQ and find its perimeter.