Practice Congruence in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

Quick Recap

Two geometric figures are congruent if they have exactly the same size and shape, so one can be placed on the other perfectly.

If you could pick up one shape and place it exactly on the other, they're congruent.

Example 1

easy
Triangle ABC has sides 3 cm, 4 cm, 5 cm. Triangle DEF has sides 3 cm, 4 cm, 5 cm. Are they congruent?

Example 2

medium
Two rectangles: Rectangle 1 has dimensions 4 cm × 6 cm. Rectangle 2 has dimensions 6 cm × 4 cm. Are they congruent? Explain.

Example 3

easy
Are a square with side 5 cm and a rhombus with side 5 cm necessarily congruent? Explain why or why not.

Example 4

hard
Triangle PQR: \angle P = 50°, \angle Q = 60°, PQ = 8 cm. Triangle XYZ: \angle X = 50°, \angle Y = 60°, XY = 8 cm. Are they congruent? Which postulate applies?
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