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Why is this concept useful?: Understanding how to prove the congruence of two shapes is important as it is a way to prove that two figures are the same size and shape.
Where does this concept fit into the curriculum?: Grade 8

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What are Congruent Shapes? Congruent shapes are shapes that have both the same size and shape. For example, in the following diagram, the two triangles are congruent as they have the same size and the same side lengths.

In congruent shapes, all sides and angles are the same between two shapes.

Sample Math Problems

Question

Consider the two triangles below. Are these two triangles congruent?

Solution

No, because the internal angles and sides must be the same for the triangles to be congruent

Question

Consider the two triangles below. Are these two triangles congruent?

Solution

Yes because the angles and sides are the same.

Question

What is the measure of angle CBD?

Solution

52 degrees. Because angle CBD corresponds to angle ACB and the two triangles are congruent.

Question

What is the measure of angle BCD?

Solution

61 degrees because angles BCD corresponds to angle ABC and the two triangles are congruent.

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