Name ________________________ Midterm Review # 1

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

SECTION I

1. What is the length of the line segment with endpoints (−6 , 4 ) and (2 , −5 )

2. Which diagram shows the construction of a30∘angle?

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

3. What is the slope of a line that is perpendicular to the line whose equation is 3 x+4 y=12?

(1)

34

(2) −3

4

(3)

43

(4) −4

3

4. If the Hexagon is rotated clockwise around its center, the minimum number of degrees it must be rotated to carry the hexagon onto itself is(1) 54∘

(2) 60∘

(3) 108∘

(4) 360∘

5. A quadrilateral whose diagonals bisect each other and are perpendicular is a

(1) rhombus(2) rectangle(3) trapezoid(4) parallelogram

6. What is an equation of the line that passes through the point (4 , −5 ) and is parallel to the line3 x+2 y=12?(1) y=−3 x+6

(2) y=3

2x+1

(3) y=3 x+1

(4) y=−3

2x+1

7. In the accompanying diagram, intersects at E and at F, and intersects at

G and at H. If , and , what is the value of x.

8. Triangle ABC has angles in the ratio of 1 :3:5 . Which type of triangle isΔ ABC ?(1) acute(2) isosceles(3) obtuse(4) right

9. Triangle ABC has vertices A (0 , 0 ) ,B (−1, 1 ) and C (7 , −5 ) . Which equation represents the perpendicular

bisector of BC ?

(1) y= 4

3x+ 7

3

(2) y=−3

4x

(3) y= 4

3x−6

(4)

y=−34

x−6

10. InΔ ABC , AB=7 , BC=8 , andAC=9 . Which list has the angles of Δ ABC in order from smallest to largest?(1) ∠ A , ∠B , ∠C(2) ∠B , ∠ A , ∠C(3) ∠C , ∠B , ∠A(4) ∠C , ∠ A , ∠B

11. In the diagram below, Δ ABC≃Δ XYZ .

Which two statements identify corresponding congruent parts for these triangles?(1) AB≃XY and ∠C≃∠Y

(2) AB≃YZ and ∠C≃∠X

(3) BC≃XY and ∠ A≃∠Y

(4) BC≃YZ and ∠ A≃∠X

12. In the accompanying diagram, E is the midpoint of AB and CD .

Triangle AEC can be proved congruent to triangle BED by

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

13. The midpoint of AB is and the coordinates of point A are What are the coordinates of point B?

(1) (2 ,15 )

(2) (2 ,−3

2 )(3)

(1 ,152 )

(4) (7,3 )

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

(Note: The diagram above is not drawn to scale)

Which statement must be true?(1) m∠ ABC<m∠CBD(2) (3) m∠ ABC<m∠C(4) m∠ ABC>m∠C+m∠D

15. In the diagram below ofΔ ABC , medians AD , 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 Δ ABC side BC is extended to point D, m∠ A=x , m∠B=2 x+15 , and m∠ ACD=5 x+5 .

What is m∠B ?(1) 5(2) 20(3) 25(4) 55

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]

17. Describe a sequence of rigid motions that will map Δ ABC onto Δ A ' ' ' B' ' ' C' ' ' .

18. The line that passes through point (2 , −5 ) and (4 , y ) has a slope of 3 . Find y.

19. Complete the proof: Isosceles Δ ABC ,AB≃AC

Prove: The base angles are congruent: ∠B≃∠C

Statements Reasons

1. Isosceles Δ ABC

,AB≃AC 1. Given

2. Draw AD

, the angle bisector of ∠ A 2. Construction

3. AD≃AD 3.

4. ∠BAD≃∠CAD 4.

5. Δ ABD≃Δ ACD 5.

6. ∠B≃∠C 6.

20. The coordinates of the vertices of parallelogram ABCD are A (−2 , 2 ) , B (3 , 5 ) , C ( 4 , 2 ) , and D (−1 , −1 ) . State the coordinates of the vertices of parallelogram A' ' B' ' C ' ' D ' '

that result from the transformation r y−axis∘T 2, −3 . [The use of the set of axes below is optional. ]

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]

21a. Find the unknown angle in the diagram.

21b. Explain how you solved for g.

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]22. Given: A( 1,1), B(0,5), C(6,7), D(5,3)Prove: ABCD is a parallelogram but not a rectangle. [The use of a grid is optional.]

23. Given: rhombus ABCD, diagonal AC extended through C to E, BE , andDE .

Prove: BE≃¿ ¿DE

24. Use a compass and straightedge to construct an inscribed square in circle T shown below. [Leave all construction marks.]