1. ANSWERS TO WORKSHEET
1) 14 2) 24 3) 53 4) 50 5) 6 7) 20 8) 25 9) 43 10) Both pairs opp. Sides cong. 11) 1 pair is cong. and parallel 12) Both opp sides are parallel 13) Diags bisect each other 14) Both pairs opp angles are cong 15)1) Given 2) CPCTC 3) Def of midpt 4) Def of seg bisector 5) Diags bisect each other Questions???

2. 5-3 Theorems Involving Parallel Lines

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

4. Example 1)If AB = 6, find BC and AC. BC = 6 AC = 12
2) If XY = 2k + 3 and XZ = 22, find k. 2k + 3 = 11 k = 4 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.

6. Theorem The segment that joins 2 midpoints of a triangle is: 6 12
Parallel to the Base
Half as long as the Base
To solve: Either—
Double OR Half 6 12

7. More Sample Pictures 20 3
1.5 10

8. Multiple Choice 5-3
Which of the following points pictured must be a midpoint?
A) A and C
B) B and C
C) A and B
D) A, B and C
ANSWER: C ● A B C

9. Watch Example on overhead!!!

10. Example X, Y, Z are midpoints of AB, BC, and AC 12 1/2k 4k + 6
If AC = 24, XY =
If AB = k, YZ =
If XZ = 2k + 3, BC =
If XY = 10 and AC = x + 2, find x. 12
1/2k
4k + 6
x + 2 = 2(10)
x = 18 B X Y C A Z

11. Homework
Page 180 #1-17
SHOW WORK!!!