Congruence Worked Solutions — GCSE Maths

Write down the correspondence the congruence statement gives

Writing triangle $ABC$ is congruent to triangle $PQR$ names the vertices in matching order, so the pairs of equal parts can be read straight off.

Match the part you want to the part you know

The part asked for corresponds to a part that is known, so the two are equal.

State the answer

So $QR = BC = 5$ cm.

Write down the correspondence the congruence statement gives

Writing triangle $ABC$ is congruent to triangle $DEF$ names the vertices in matching order, so the pairs of equal parts can be read straight off.

Match the part you want to the part you know

The part asked for corresponds to a part that is known, so the two are equal.

State the answer

So $EF = BC = 6$ cm.

Write down the correspondence the congruence statement gives

Writing triangle $XYZ$ is congruent to triangle $LMN$ names the vertices in matching order, so the pairs of equal parts can be read straight off.

Match the part you want to the part you know

The part asked for corresponds to a part that is known, so the two are equal.

State the answer

So $MN = YZ = 13$ cm.

Write down the correspondence the congruence statement gives

Writing triangle $ABC$ is congruent to triangle $PQR$ names the vertices in matching order, so the pairs of equal parts can be read straight off.

Match the part you want to the part you know

The part asked for corresponds to a part that is known, so the two are equal.

State the answer

So $RP = CA = 10$ cm.

Write down the correspondence the congruence statement gives

Writing triangle $ABC$ is congruent to triangle $PQR$ names the vertices in matching order, so the pairs of equal parts can be read straight off.

Match the part you want to the part you know

The part asked for corresponds to a part that is known, so the two are equal.

State the answer

So $\angle QPR = \angle BAC = 63^\circ$.