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???
5-3 THEOREMS INVOLVING
PARALLEL LINES
THEOREM

If three parallel lines cut off congruent segments
on one transversal, then they cut off congruent
segments on every transversal.
X
A
B
C
If AB = BC
then XY = YZ
Y
Z
EXAMPLE
1)If AB = 6, find BC and
AC.
BC = 6
AC = 12
A
B
C
2) If XY = 2k + 3 and
XZ = 22, find k.
2k + 3 = 11
k=4
X
Y
Z
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.
THEOREM

The segment that joins 2 midpoints of a triangle
is:
Parallel to the Base
 Half as long as the Base
 To solve: Either—
Double OR Half

6
12
MORE SAMPLE PICTURES
3
20
10
1.5
Multiple Choice 5-3
Which of the following points pictured must be a
midpoint?
A)
B)
C)
D)
A and C
B and C
A and B
A, B and C
ANSWER: C
●
A
C
B
Watch Example on overhead!!!
EXAMPLE

X, Y, Z are midpoints of AB, BC, and AC
 If AC = 24, XY = 12
 If AB = k, YZ = 1/2k
 If XZ = 2k + 3, BC = 4k + 6

If XY = 10 and AC = x + 2, find x. x + 2 = 2(10) x = 18
B
Y
X
C
Z
A
HOMEWORK

Page 180 #1-17

SHOW WORK!!!