Question

Corresponding angles of ΔABC and ΔDEF are congruent. Does this prove that the triangles are congruent? Justify.

A) yes; AAA guarantees that all corresponding parts of the two triangles are congruent.

B) yes; AAA guarantees similarity and congruency because the triangles must have equal sides to have equal angles.

C) no; AAA only guarantees similarity because the lengths of the sides of the two triangles are not necessarily equal.

D) yes; AAA guarantees congruency because if at least two angles of a triangle are congruent to each other, then the triangles are congruent.

Answer 1

The correct option is C.

Explanation:

The required answer is "no".

It is given that corresponding angles of ΔABC and ΔDEF are congruent. It means

`\angle A\cong \angle D`

`\angle B\cong \angle E`

`\angle C\cong \angle F`

From this information we can say that by AAA property of similarity

ΔABC
`\sim` ΔDEF

The lengths of the sides of the two triangles are not necessarily equal.

Since the property AAA only guarantees similarity, therefore the corresponding angles of ΔABC and ΔDEF are congruent does not prove that the triangles are congruent.

The properties of congruent triangle are : SSS, SAS, ASA, AAS.

It means at least one side is required to say that the triangles are congruent.

Option C is correct.

Answer 2

NO. Three congruent angles only proves the triangles are similar. You must have at least one side length to prove congruency.

SSS, SAS, ASA, AAS prove triangle congruency.

Answer: C