Congruence and corresponding parts

Three quick questions from earlier lessons.

$\triangle ABC \cong \triangle DEF$ . Which angle of $\triangle DEF$ matches $\angle B$ ?

Congruent figures match part for part.

Two figures are congruent if a sequence of rigid transformations maps one onto the other. Then corresponding sides and angles are equal. In

\triangle ABC \cong \triangle DEF

the order of letters gives the correspondence:

A \leftrightarrow D

,

B \leftrightarrow E

,

C \leftrightarrow F

.

$\triangle PQR \cong \triangle STU$ , $PQ = 7$ , $\angle R = 40^\circ$ .

ST = 7

P↔S, Q↔T.

\angle U = 40^\circ

R↔U.

Your turn: $\triangle ABC \cong \triangle XYZ$ and $BC = 12$ . Find $YZ$ .

YZ = 12

B↔Y, C↔Z.

$\triangle ABC \cong \triangle DEF$ with $AB = 3$ , $BC = 11$ and $CA = 18$ . Find $DE$ .
$\triangle ABC \cong \triangle DEF$ with $AB = 9$ , $BC = 15$ and $CA = 16$ . Find $DE$ .

$\triangle KLM \cong \triangle STU$ . Which segment corresponds to $LM$ (length 5)?
1. $TU$
2. $ST$
3. $SU$

$\triangle PQR \cong \triangle XYZ$ , with $\angle Q = 43^\circ$ and $\angle R = 40^\circ$ . Find $\angle X$ , in degrees.
$\triangle PQR \cong \triangle XYZ$ , with $\angle Q = 37^\circ$ and $\angle R = 47^\circ$ . Find $\angle X$ , in degrees.

Three questions to check you have got it.

$\triangle ABC \cong \triangle DEF$ with $AB = 3$ , $BC = 11$ and $CA = 18$ . Find $DE$ .
$\triangle ABC \cong \triangle DEF$ with $AB = 9$ , $BC = 15$ and $CA = 16$ . Find $DE$ .
$\triangle ABC \cong \triangle DEF$ with $AB = 4$ , $BC = 11$ and $CA = 17$ . Find $DE$ .

Corresponding parts

The order of letters in a congruence statement gives the matching.

Watch out: match by position, not by appearance.

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