10C

Congruent figures and congruent triangles

Congruent figures and matching sides and angles, and the four tests for congruent triangles SSS, SAS, AAS and RHS.

Congruent figures

Congruent figures have matching (corresponding) sides equal and matching angles equal. In $\triangle ABC \equiv \triangle PQR$, the order of letters shows the matches: $A \leftrightarrow P$, $B \leftrightarrow Q$, $C \leftrightarrow R$.

The four tests

Example 1●●

$\triangle ABC$ has $AB = 5$, $BC = 7$, $\angle B = 40^\circ$. $\triangle DEF$ has $DE = 5$, $EF = 7$, $\angle E = 40^\circ$. Are they congruent?

Two sides and the included angle match.

Yes, by SAS: $\triangle ABC \equiv \triangle DEF$.

Flashcards

The four tests

SSS, SAS, AAS, RHS

Is AAA a test?

No, it gives similar triangles.

$equiv$

is congruent to

Practice

$AB = 5$, $BC = 7$, $\angle B = 40^\circ$ and $DE = 5$, $EF = 7$, $\angle E = 40^\circ$. Which test?
Two right-angled triangles have hypotenuse $13$ and another side $5$. Which test?
Two triangles each have sides $4, 6, 9$. Which test?
Two triangles have angles $50^\circ$ and $60^\circ$, and the side opposite $50^\circ$ is $8$ in both. Which test?
Two triangles both have angles $30^\circ, 60^\circ, 90^\circ$. Are they definitely congruent?
If $\triangle ABC \equiv \triangle PQR$, which side matches $BC$?
$\triangle ABC \equiv \triangle XYZ$ with $\angle A = 50^\circ$ and $\angle B = 60^\circ$. Find $\angle Z$.
Congruent shapes have: