Learn what it means for two shapes to be exactly identical, and the rules that prove two triangles are congruent.
Two figures are congruent if they have exactly the same shape and size — one can be placed perfectly on top of the other. For triangles, this means all corresponding sides and angles are equal.
Triangle ABC has sides 5cm, 6cm, 7cm. Triangle PQR has sides 5cm, 6cm, 7cm. Are they congruent?
Yes, since all corresponding sides are equal (SSS)
If two triangles are congruent, what can you say about their areas?
They must be equal, since congruent shapes are identical
Common congruence rules include SSS (all three sides equal), SAS (two sides and the included angle equal), ASA (two angles and the included side equal), and RHS (right angle, hypotenuse, and one side equal, for right triangles).
Two triangles have two pairs of equal sides and the angle between them is also equal. Which rule proves congruency?
SAS (Side-Angle-Side)
Two right triangles have equal hypotenuses and one equal leg. Which rule proves congruency?
RHS (Right angle-Hypotenuse-Side)
1. Two triangles have all three angles equal but different side lengths. Are they necessarily congruent?
2. Two triangles share two equal angles and the side between them is also equal. Which rule applies?
3. Triangle DEF has sides 4cm, 4cm, 4cm. Triangle GHI has sides 4cm, 4cm, 4cm. Are they congruent?
4. Two right triangles both have a right angle, equal hypotenuse of 10cm, and one equal leg of 6cm. Which rule proves congruency?
5. If triangle ABC is congruent to triangle XYZ, and angle A is 40°, what is angle X?