The four conditions that prove two triangles are congruent, the two that do not, and how to write a short proof.
What you will learn
- Use SSS, SAS, ASA and RHS
- Spot facts that do not prove congruence
- Find missing sides and angles in congruent triangles
- Write a congruence proof with reasons
Same shape, same size
Two shapes are congruent if one fits exactly on top of the other, perhaps after turning or flipping it.
Translations, reflections and rotations always give congruent images. Two triangles are congruent if they share any one of these sets of facts:
- SSS: all three sides are equal.
- SAS: two sides and the angle between them are equal.
- ASA: two angles and the side between them are equal. (Because the third angle then matches too, any side in the same position will do; some books call that AAS.)
- RHS: both have a right angle, equal hypotenuses and one other equal side.
The rest of this lesson and its 8 practice questions are locked.
In this lesson
- Same shape, same size
- Facts that are not enough
- Using congruent triangles
- Writing a proof
- Try it: First question
8 practice questions, marked as you go; about 20 minutes in all.
Key terms
Congruent, Three equal angles
In this unit: Transformations, congruence and similarity
Translations, reflections, rotations and enlargements on a grid and how to describe them fully, combined transformations and invariant points, the congruence conditions, and similar shapes with their length, area and volume scale factors.