Proving Similarity Using Side-Side-Side (SSS) Postulate

Proving two triangles congruent by using only side lengths is called proving them similar by the Side-Side-Side (SSS) __________.

This method involves demonstrating that all corresponding sides of the triangles are __________.

Once you establish this congruence, you can conclude that the triangles have the same __________.

To find whether the given triangles are congruent, we need to check if their corresponding sides are __________.

AB = 10 cm corresponds to DE = __________ cm.

Since all corresponding sides are equal, by the Side-Side-Side (SSS) __________, we can say that the two triangles are congruent.

Proving two triangles congruent by using only side lengths is called proving them similar by the Side-Side-Side (SSS) Postulate. This method involves demonstrating that all corresponding sides of the triangles are congruent. Once you establish this congruence, you can conclude that the triangles have the same shape. Here's a detailed analysis of how to prove SSS congruence:

Problem: Consider the following two triangles: Triangle ABC with sides AB = 10 cm, AC = 7.5 cm, and BC = 6.5 cm; and Triangle DEF with sides DE = 10 cm, DF = 7.5 cm, and EF = 6.5 cm. Are these triangles congruent? Justify your answer.

Solution: To find whether the given triangles are congruent, we need to check if their corresponding sides are equal. Let's compare each triangle side by side:

AB = 10 cm corresponds to DE = 10 cm.
AC = 7.5 cm corresponds to DF = 7.5 cm.
BC = 6.5 cm corresponds to EF = 6.5 cm.

Since all corresponding sides are equal, by the Side-Side-Side (SSS) Postulate, we can say that the two triangles are congruent. Therefore, the statement "the given triangles are congruent" is true.

Learn how to prove two triangles congruent by using only side lengths through the Side-Side-Side (SSS) Postulate. Understand the process of checking if the corresponding sides of two triangles are equal to establish congruence.