Triangle Proportionality Theorem Examples

If AD = 3, DC = 8, and CG = 24, what is the length of BG?

Unlike our favorite 70's trio, we can solve for this BG by setting up and solving a proportion.

8 × BG = 3 × 24
8 × BG = 72
BG = 9

If AD = 10, DF = 12, and EH = 8, how long is HF?

No magic required for this one. Just set up a proportion.

10 × HF = 12 × 8
10 × HF = 96
HF = 9.6

If DH = 2x + 4, HG = 3, DF = 4x – 1, and FC = 5, what is the value of x?

Sorry, the answer is not 25, nor is it 6, nor is it 4. Just guessing numbers you can find in the titles of songs from the 70's will not help. What will help is setting up a proportion and then solving it.

10x + 20 = 12x – 3
23 = 2x
11.5 = x