Question

(a) Show with an example that two triangles can't be congruent using AAA criterion.

(b) Which congruence criterion will you use in the following?

Given: AC = DF

AB = DE

BC = EF

So, ΔABC ≅ ΔDEF

[3 MARKS]

Answer 1

(a) Proof: 2 Marks
(b) Answer: 1 Mark



(a)Consider the two triangles :

In the two triangles,

$\angle ABC$ = $\angle PQR$

$\angle BAC$ = $\angle QPR$

$\angle ACB$ = $\angle PRQ$

But clearly, $\Delta ABC$ is not congruent to $\Delta PQR$.
As the sides of triangle are not equal.
Thus, AAA cannot be a congruence condition.

It actually tells that the two triangles are similar, but not congruent.

(b) Since, the three sides of the first triangle is equal to the corresponding three sides of the second triangle, by SSS congruence criterion ΔABC is congruent to ΔDEF.