Proving Congruence of Isosceles Triangles: Using the Side-Side-Side (SSS) Criterion

If the congruent sides in one isosceles triangle have the same measure as the congruent sides inanother isosceles triangle, then the triangles are congruent

To prove that two triangles are congruent, we need to show that all corresponding sides and angles are equal

To prove that two triangles are congruent, we need to show that all corresponding sides and angles are equal. In the case of isosceles triangles, we can use the fact that the congruent sides have the same measure to prove congruence.

Let’s say we have two isosceles triangles, Triangle ABC and Triangle DEF. We know that Triangle ABC has sides AB = AC, and Triangle DEF has sides DE = DF. We want to prove that Triangle ABC is congruent to Triangle DEF.

To prove congruence, we can use the Side-Side-Side (SSS) congruence criterion. According to this criterion, if the measures of the three sides of one triangle are equal to the measures of the corresponding three sides of another triangle, then the triangles are congruent.

In this case, we have AB = DE, AC = DF, and BC = EF. Since all three pairs of corresponding sides have the same measures, we can conclude that Triangle ABC is congruent to Triangle DEF based on the SSS criterion.

Therefore, if the congruent sides in one isosceles triangle have the same measure as the congruent sides in another isosceles triangle, then the triangles are congruent.

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