PAIBOTLearn
Sign inSign up

Proofs with similar triangles

Constructions & proofs

Japanese school year: Junior high 3

What you learn

Learn how to construct logical proofs establishing segment ratios and equal angles based on triangle similarity criteria. This method builds on parallel line properties and congruence proofs by focusing on proportional sides and corresponding angles. It is essential for solving complex geometry problems and analyzing spatial relationships.

Go to practice

Key points

These conditions prove two triangles are similar. They are similar if all 3 pairs of corresponding side ratios, 2 pairs of side ratios and their included angle, or 2 pairs of angles are equal.

This is a common strategy for similarity proofs. Proving two pairs of angles are equal by finding shared angles or corresponding/alternate angles from parallel lines is usually the most direct method.

This rule applies when using the similarity symbol ∼\sim. Always write the triangle vertices in matching order, such as △ABC∼△DEF\triangle ABC \sim \triangle DEF, to keep corresponding parts clear.

Choose a set to practice.