Angles in triangles (age 12+)
Know and use the criteria for triangle congruence (SSS, SAS, ASA, RHS), use standard labelling conventions for sides and angles of triangle ABC, and determine whether two triangles are congruent
What a learner can do afterwards
- State which congruence criterion (SSS, SAS, ASA, or RHS) applies to a given pair of triangles
- Use the notation △ABC ≅ △DEF and match corresponding sides and angles
- Determine whether given measurements produce a unique triangle, more than one, or none
The lesson
Every triangle has three vertices, named with capital letters like A, B, and C. Each side gets the matching lowercase letter of the vertex across from it. Side a is opposite angle A, side b is opposite angle B, and side c is opposite angle C.
Two triangles are congruent when they are exactly the same size and shape, even if one is turned or flipped. We write this as triangle ABC is congruent to triangle DEF. The letter order matters: A matches D, B matches E, C matches F. That tells you side AB equals side DE, and angle B equals angle E.
Triangle ABC has sides 5 cm, 6 cm, and 7 cm. Triangle DEF has sides 5 cm, 6 cm, and 7 cm too, matched in the same order. All three pairs of sides match, so the triangles are congruent by SSS (side-side-side). You do not even need to check the angles.
Four checks prove congruence: SSS (all three sides match), SAS (two sides and the angle between them match), ASA (two angles and the side between them match), and RHS (a right angle, the hypotenuse, and one other side match). The side or angle in the middle of the name must sit between the other two, not off to the side.
Match corresponding vertices in order, then check SSS, SAS, ASA, or RHS to prove two triangles are congruent.
Watch it
Where it sits
This opens up
Nothing builds on it yet.
Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
8 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.