Congruent Shapes

Congruent Shapes: What to Look For

Two shapes are congruent if they have exactly the same size and shape. That means matching sides are equal in length and matching angles are equal in measure. A shape may be turned, flipped, or moved, but it is still congruent if nothing has been stretched or resized.

How to Solve

1. Match the vertices carefully. Start by pairing a corner on one shape with the corresponding corner on the other.
2. Compare side lengths and angles. Check that each side in one shape matches the correct side in the other, and that the angles line up.
3. Use the given information. If some lengths or angle measures are labeled, use them to identify the matching parts.
4. Write the final result clearly. If the task asks for a missing length, angle, or statement about congruence, give the simplified exact answer.

Good Check

After solving, verify that every matched pair agrees: equal sides with equal sides, equal angles with equal angles. If one value does not match, the shapes are not congruent or the correspondence is incorrect.

Tip

Be careful with orientation. A rotated or reflected figure can still be congruent, so focus on the matching parts, not just the visual position.