1. Theorems Involving Parallel Lines
Section 5-3

2. Goals
We will apply theorems about parallel lines and the segment that joins the midpoints of two sides of a triangle.

3. Theorem 5-8
If two lines are parallel, then all points on one line are equidistant to the other line.
5 ft
5 ft
5 ft

4. Theorem 5-9
If three parallel lines cut off congruent segments on one transversal, then they cut off congruent segments on every transversal.

5. Practice Find the values of x and y if P is the midpoint of AB 3x – 14

6. Practice Find the values of x and y if P is the midpoint of AB
3x – 14 = 2x – 1
3x – 14
x – 14 = -1
x = 13
2x – 1
2y + 10 = 6y – 30
10 = 4y – 30
40 = 4y
10 = y
y = 10
2y + 10
6y – 30 A P B

7. Practice (Example 1 on sheet)
AR BS CT, and RS = ST
Complete:
a. if RS = 12, then ST = ____
b. if AB = 8, then BC = ____
c. if AC = 20, then AB = ____
d. if AC = 10x, then BC =____ R A S B T C

8. Theorem 5-10
A line that contains the midpoint of one side of a triangle, and is parallel to another side, will pass through the midpoint of the third side.
parallel

9. Theorem 5-11
A segment that joins the midpoints of two sides of a triangle:
1.) is parallel to the third side
2.) is half as long as the third side

10. Practice
Find the value of w and z.
(3z + 1)cm
38˚
8cm
70˚
2w˚

11. Practice Find the value of w and z. w = 36 z = 5 (3z + 1)cm 38˚ 8cm
70˚
2w˚

12. Practice (Example 2 on sheet)
R, S, and T are midpoints of the sides of triangle ABC B R S A T C
Complete the table.
AB BC AC ST RT RS

13. Back to Parallelograms
Practice
R, S, and T are midpoints of the sides of triangle ABC B R S A T C
Complete the table.
AB BC AC ST RT RS 6 7 9 20
7.5 11
Back to Parallelograms 18
15.6 5