7.5

Proportions in Triangles

Side Splitter Theorem Corollary to the Side Splitter Triangle-Angle-Bisector Theorem

Side-Splitter Theorem

If a line is parallel to one side of a triangle and intersects the other two sides, then it divides those sides proportionally.

XR RQ



YS SQ

X R Q S Y

#1 Using the Side-Splitter Theorem



x

Find the value of

x

.

 1 .

5  5

x

2 .

5 5 2.5(x + 1.5) = 5x

x

+ 1.5

2.5x + 3.75 = 5x

x

3.75 = 2.5x

1.5 = x 2.5

Corollary to the Side-Splitter Theorem

 If three parallel lines intersect two transversals, then the segments intercepted on the transversals are proportional.

a b



c d b a c d

#2 Using the Side-Splitter Theorem

 Solve for

x

and

y

.

16 .

5

y

 15 26 15

y

 429

y

 28 .

6

x

30  15 26 26

x

 450

x

 17 .

3 16.5

15

x y

26 30

Triangle-Angle Bisector Theorem

 If a ray bisects an angle of a triangle, then it divides the opposite side into two segments that are proportional to the other two sides of the triangle.

B D

AC



AD

A

CB DB

C

#3 Using the Triangle-Angle Bisector Theorem

 Find the value of

y

.

5 8  3 .

6

y

5

y

5

y

 8 ( 3 .

6 )  28 .

8

y

 5 .

76 5 3.6

8

y

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Smartboard problems

Your Assignment 7.5 Practice Worksheet