Similar Triangles Explained

Similar triangles have the same shape but not necessarily the same size. They are powerful because corresponding sides stay proportional.

Quick idea

If triangles are similar, matching angles are equal and matching side lengths form equal ratios.

Steps

1. Match corresponding angles or sides.
2. Set up a proportion using corresponding side lengths.
3. Solve the proportion for the unknown side.
4. Check that the larger triangle has consistently larger matching sides.

Worked example

Use similar triangles to find a missing side.

Full solution

Step-by-step walkthrough

Step 1

Match sides that sit in the same relative position.

Step 2

Write the side ratios as a proportion.

Step 3

Cross multiply or scale to solve the missing side.

Common mistake

Do not mix corresponding sides. The order of the ratio must match the same triangle relationship each time.

Practice problems

1. If small/large scale is 2/5 and a small side is 6, find the large side.
2. If triangles are similar and one side doubles, what happens to all matching sides?
3. If AB matches DE, what should BC match in the same order?

Answers

1. 15
2. They double
3. EF

Ask Pennpaper to explain it live

If the steps make sense but you still feel stuck, start a Pennpaper lesson and ask the tutor to draw the problem on the whiteboard. Seeing the symbols move step by step is often what makes the concept click.

Related guides

• How to Solve Proportions
• Pythagorean Theorem Explained
• Congruent Triangles: SSS, SAS, ASA, AAS