Midterm Review #2 Name: ___________________________Geometry Pd. _____ Midterm Review

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

1. What is the distance between the points (-5,3) and (-3,1)?1) 2√172) 2√53) 2√24) √10

2. The diagram below shows the construction of the bisector of .

Which statement is not true?

3. Line m and point P are shown in the graph below.

Which equation represents the line passing through P and parallel to line m?1)2)3)

4)

5. A parallelogram must be a rectangle when its1) diagonals are perpendicular2) diagonals are congruent3) opposite sides are parallel

1) 3)

2) 4)

4) opposite sides are congruent

6. A quadrilateral has vertices with coordinates , , , and . Which type of quadrilateral is this?1) rhombus2) rectangle3) square4) trapezoid

7. Which statement is sufficient evidence that is congruent to ?

1) and

2) , ,

3) There is a sequence of rigid motions that maps onto , onto , and onto .

4) There is a sequence of rigid motions that maps point A onto point D, onto , and onto .

8. Two angles in a linear pair are in a 7:3 ratio. What is the measure of one of the angle?(1) 180 degrees(2) 18 degrees(3) 10 degrees(4) 126 degrees

9. In the diagram below of isosceles , the measure of vertex angle B is 80°. If extends to point D, what is ?

1) 502) 803) 1004) 130

10. Which equation represents the perpendicular bisector of whose endpoints are and ?

1)2)

3)

4)

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

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

12. Steve drew line segments ABCD, EFG, BF, and CF as shown in the diagram below. Scalene is formed.

Which statement will allow Steve to prove ?1)2)3)4)

13. In the accompanying diagram, bisects and . What is the most direct method of proof that could be used to prove ?1)2)3)4)

14. The midpoint ofAB is M(2,6) If the coordinates of A are (4,11),what are the coordinates of B?(1) (3, 8.5)

(2) (2,5)

(3) (0,1)

(4) (6, 16)

15. Which statement best describes the lines whose equations are: y = 2x+5 and x+2y = -2

16. What is the measure of each exterior angle of an octagon?(1) 360(2) 45(3) 1080(4) 135

1) They are perpendicular to each other.2) They are segments.3) They are parallel to each other.4) They intersect each other.

17. If the measures, in degrees, of the three angles of a triangle are x, , and , the triangle must be1) obtuse2) equiangular3) right4) Acute

18. Which geometric principle is used to justify the construction below?

1) A line perpendicular to one of two parallel lines is perpendicular to the other.

2) Two lines are perpendicular if they intersect to form congruent adjacent angles.

3) When two lines are intersected by a transversal and alternate interior angles are congruent, the lines are parallel.

4) When two lines are intersected by a transversal and the corresponding angles are congruent, the lines are parallel.

19. In the diagram below, which transformation was used to map to ?

1) dilation2) rotation3) reflection4) glide reflection

Part 2, 3 and 4 Short Answer.

20. In parallelogram ABCD shown below, diagonals and intersect at E.

Prove:

21. Given: Quadrilateral ABCD is a parallelogram with diagonals and intersecting at E

Describe a single rigid motion that maps onto .

22. Triangle ABC has vertices A(-2,3), B(5,1), and C(3,-5). State the coordinates of the image of under the composition T 0 ,−2 °r origin

23. In the accompanying diagram of right triangles ABD and DBC, , , and . Find the length of

, leave answer in simplest radical form.

24. In the diagram of parallelogram FRED shown below, is extended to A, and is drawn such that .

If , what is ?

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

26. The coordinates of quadrilateral JKLM are J (1,-2), K(x,2) ,L (6, 8), and M (-2, 4).

a) Determine what the value of x must be to make JKLM a parallelogram, and plot it.

b) Prove that JKLM is a parallelogram

c) What other type of quadrilateral is JKLM? Why?

27. Given: ¿ Z≅<X , WY bisects∠ZWX Prove: Y isthemidpoint of XZ

Statements Reasons

1. ¿ Z≅<X , WY bisects∠ZWX 1. Given

2. 2.

3. 3.

4. 4.

5. 5.

6. 6.

28) Find the unknown angle in the diagram below: