Take note Corollary: Corollary to the Side-Splitter Theorem

Corollary

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

If …

a ∥ b ∥ c eh parallel to , b parallel to , c

Then …

A B B C = W X X Y fraction eh b , over b c end fraction . equals . fraction w x , over x y end fraction

You will prove the Corollary to Theorem 7-4 in Exercise 46.

Problem 2 Finding a Length

Camping Three campsites are shown in the diagram. What is the length of Site A along the river?

Let x be the length of Site A along the river.

x 8 = 9 7.2 Corollary to the Side-Splitter Theorem 7.2 x = 72 Cross Products Property x = 10 Divide each side by  7.2. table with 3 rows and 3 columns , row1 column 1 , x over 8 , column 2 equals , 9 over 7.2 , column 3 cap corollarytothecap sideminuscap splittercap theorem , row2 column 1 , 7.2 x , column 2 equals 72 , column 3 cap crosscap productscap property , row3 column 1 , x , column 2 equals 10 , column 3 cap divideeachsideby . 7.2. , end table

The length of Site A along the river is 10 yd.

✓ Got It?

2. What is the length of Site C along the road?

Take note Theorem 7-5: Triangle-Angle-Bisector Theorem

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.

If …

A D → eh d vector  bisects ∠ C A B angle c eh b

Then …

C D D B = C A B A fraction c d , over d b end fraction . equals . fraction c eh , over b eh end fraction

You will prove the Triangle-Angle-Bisector Theorem in Exercise 47.