Name _____________________________ Date _____________Geometry Period _____________

: Parallel Lines and Transversals1. In the diagram, which condition ensures that lines and are parallel?

A.B.C.D.

2. Lily used properties of parallel lines to conclude that Which other result is Lily able to conclude?

A.B.C.D.

3. In the diagram below, andWhich of the following statements must be true?

A.

B.C.D.

4. In the figure below, lines l and m are parallel lines cut by transversal line p.

Jackie said that if <1=110 degrees then <2=110 degrees as well. Which of the following justifies Jackie’s statement?

A. Alternate exterior angles are congruent.B. Alternate interior angles are congruent.C. Corresponding angles are congruent.D. Vertical angles are congruent.

Name _____________________________ Date _____________Geometry Period _____________5. In the diagram below, Transversals t and v intersect Parallel Lines m and n at Point R.

What is the value of x?

A. 42B. 48C. 132D. 138

6. Given: PQRS is a parallelogram; S, P, and T are collinear.Prove: 1 4.

Statements Reasons

1. PQRS is a parallelogram; S, P, and T 1. Given are collinear 2. 2. Definition of a parallelogram3. 1 3 3. Parallel lines cut by a transversal form congruent corresponding angles4. 4. Definition of a parallelogram5. 4 3 5. ?6. 1 4 6. Transitive property of congruence

Which reason could be used to justify Statement 5?

A. Angles that are supplements of the same angle are congruent to each other.B. Parallel lines cut by a transversal form congruent alternate interior angles.C. Parallel lines cut by a transversal form congruent corresponding angles.D. Intersecting lines form congruent vertical angles.

7. Edwardo sketched two intersecting lines. He named the angles that were formed and with and as vertical angles. Which of these statements is always true?

A.B.C.D.

8. In this figure, lines a, b, c, d, and e intersect as shown.Based on the angle measures, which pair of lines is parallel?

A. a and bB. c and eC. c and dD. d and e

Name _____________________________ Date _____________Geometry Period _____________9. Consider the statement. If WX = YZ, then YZ = WX. Which property can be used to justify the statement?

A) Reflexive B) transitive C) symmetric D) multiplication

Open Ended:#10) Use the figure to determine whether each pair is intersecting, parallel or skew.

a. b.

c. d.

For #11 – 13: In the figure, l ∥ m. Use the words alternate interior, alternating exterior, consecutive interior, and corresponding to determine the relationship between each pair of angles.

11) ∠3 and ∠9

12) ∠4 and ∠8

13) ∠14 and ∠6

For #14-16: Use the diagram to find the missing variables.

#14) Given , , find x. Make sure to explain.

#15) Find the values for x, y, and z. Make sure to explain

10 9 8 7

1 2

3 4

5 6

l m

1

7

34 5 6

128109

11

2

13 14

l

m

Name _____________________________ Date _____________Geometry Period _____________

x = ________ y = ________ z = ________

#16) Find the values for x, y, and z. Make sure to explain

x = ________ y = ________ z=_____________

18) Complete the following proof.

C7z

5y+7

82°2x

D

EF

A B

G H

5z+2 x

68°4y

Name _____________________________ Date _____________Geometry Period _____________

Directions: Complete the following proofs. At least 2 of them need to be completed as formal proofs. The others may be informal proofs.

19)

20)

Name _____________________________ Date _____________Geometry Period _____________21)

22)

23)

Name _____________________________ Date _____________Geometry Period _____________For the following proofs use the diagram below

24) Show: <3=<23

25) Show: <1 and <24 are supplemenatary

26) Show: <14 and <11 are supplementary

27) Show: <11=<13

Name _____________________________ Date _____________Geometry Period _____________Honors:28) Given l || m, find the value(s) of x and each angle. Be sure to check for extraneous solutions.

29) Given p || t, find the value(s) of each variable and each angle.