1. 5.3 Theorems Involving Parallel Lines
Geometry
5.3 Theorems Involving
Parallel Lines

2. 4 UsefulTheorems
Today you will learn 4 useful theorems about parallel lines. These will help you solve problems and write proofs.

3. Theorem
If 2 lines are parallel, then all points on one line are equidistant from the other line. A B
AC = BD l m C D

4. Theorem
If 3 parallel lines cut off congruent segments on one transversal, then they cut off congruent segments on every transversal.
If AB = BC
then XY = YZ A X B Y C Z

5. Theorem
A line that contains the midpoint of one side of a triangle and is parallel to another side passes through the midpoint of the third side. X
If M is the midpoint of XY
then N is the midpoint of XZ M N Y Z

6. Theorem A segment that joins the midpoints of 2 sides of a triangle;
1. is parallel to the third side.
2. is half as long as the third side. X
MN YZ
MN = ½YZ M N Y Z

7. Find x when PQ = 3x – 9 and QR = 2x – 2.
Sample Problems:
Find x when PQ = 3x – 9 and QR = 2x – 2.
Find PR and PS when PQ = 5.
Find RS when PS = 33.
Find x when PR = x + 8 and QS = 3x – 2.
5) Find QS in problem #4. A D C B P Q R S

8. 6) Name the points shown that MUST be midpoints of the sides of the large triangle.X Y 6 A B C Z X Y 6 A B C Z 5 3 X Y 5 A B C Z 6 4

9. Find YZ if MN = 8. Find MN if YZ = 30. Find YZ if MN = 2k + 3.
10) Find MN if YZ = k. X Y Z M N

10. 11) Find x, MN and YZ if MN = x and YZ = 3x – 25.

11. 13) Find x and y if AB = 19, BC = x + 3y, and CD = 6x – y.P Q R S

12. Homework
P. 180 #1-17

13. Let’s Try A Few Together
Practice 18 # 6
Test 18 #2, 11, 12