← Mathematics — Grade 8/Geometry & the Theorem of Pythagoras

Congruent Shapes

≈ 20 min

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Two shapes are congruent if they are exactly the same shape and size — one could be placed perfectly on top of the other (after sliding, turning or flipping). In congruent figures, every pair of corresponding sides is equal and every pair of corresponding angles is equal.

For triangles you do not need to check all six measurements. Certain minimum conditions guarantee congruence — for example SSS: if the three sides of one triangle equal the three sides of another, the two triangles must be congruent.

Note

Congruent means identical in size and shape. If two triangles are congruent, matching sides and matching angles are equal — so you can read off an unknown length directly.

Worked example. $\triangle ABC$ is congruent to $\triangle DEF$ . If $AB = 5$ cm, then the corresponding side $DE$ must also be $5$ cm.

Two shapes are congruent if they have…

the same shape only

the same shape and the same size

the same area only

the same colour

$\triangle ABC$ is congruent to $\triangle DEF$ . If $AB = 5$ cm, what is the length of the corresponding side $DE$ , in cm?

Which condition is enough to prove two triangles congruent?

Two angles are equal

SSS: all three pairs of sides are equal

They have the same perimeter

One pair of sides is equal

In two congruent triangles, the corresponding angles are…

equal

supplementary

always different

always $60^\circ$

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