Section 5 3 Theorems Involving Parallel Lines Theorem

Section 5 -3: Theorems Involving Parallel Lines

Theorem 1: If 2 lines are parallel, then all equidistant points on one line are _______ from the other line. 1. What do you think equidistant means? equally distant __________________

2. According to theorem on the previous 4 and y = ____. 4 slide, x = ____, 3. Why do you think 3 lines were drawn perpendicularly to the 2 parallel lines? So they are all the same distance. ___________________

Theorem 2: If 3 parallel lines cut off congruent segments on one transversal, then they cut off congruent _________ segments on every transversal. x= 7 y= 6 z= 8

4. According to Theorem 5 -9 on the previous slide, x = ____, 8 7 y = _____, 6 and z = _____. 5. Solve for a. 5 a = 15 a=3

midpoint A B C D E AD = DE

7 and BC = _____. 7 7. If AC = 14, then AB = _____ 14 and AE = _____. 28 8. If AD = 14, then DE = _____ Theorem 4: The segment that joins the midpoints of 2 sides of a triangle: 1. ______________ is parallel to the third side. is half as long as the third side. 2. ______________

A B C D E BD CE 24

AB a. c. AC ST RT RS 6 7 9 7. 5 11 20 18 15. 6 5 12 b. BC 10 14 18 15 22 10 9 7. 8

12 8 5 x

12 4 k + 6 48

M and L 12 3 6 x + 2 = 2(10)

HOMEWORK: Page 180 #2 -16 even