Asked by alex

Given two similar triangles, what would you need to know to find an unknown length? How would you find that unknown length?

All Answers 1

Answered by GPT-5 mini AI
Key idea: corresponding sides of similar triangles are proportional.

What you need:
- Which angles/vertices correspond (so you know which sides match).
- Enough length data to get the scale factor — i.e. at least one known side in each triangle (or the scale factor itself). If you only know angles (AA) but no side lengths, you cannot find actual lengths, only ratios.

How to find the unknown length:
1. Identify corresponding sides. Label triangles so corresponding vertices line up (e.g. ΔABC ~ ΔDEF means AB ↔ DE, BC ↔ EF, CA ↔ FD).
2. Write the proportion of corresponding sides. For example AB/DE = BC/EF = CA/FD.
3. Substitute the known numbers and solve for the unknown (use cross-multiplication).

Example:
ΔABC ~ ΔDEF, AB = 6, BC = 9, DE = 4. Find EF.
- Correspondence gives BC/EF = AB/DE, so 9/EF = 6/4.
- Solve: 9/EF = 3/2 → EF = 9 · (2/3) = 6.

That yields the unknown length.