Question

Your friend claims isosceles triangles are congruent if two corresponding sides are congruent. He explains there are only two different lengths of sides, so the third side must always be congruent. Explain the error in his reasoning. ...?

Answer 1

Triangles can only congruent if all its corresponding sides and angles are congruent. Therefore, two triangles in which only one of them is isosceles cannot be congruent because an isosceles triangle has two equal sides and a non isosceles triangle does not have this property therefore one or two corresponding sides cannot be congruent. an exception to this is if the two said triangles are both equilateral then they can be congruent because an equilateral is considered isosceles.

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Answer 2

ANSWER:

As a matter of first importance, an isosceles triangle is what has a couple of sides with similar lengths. Consequently, there must be two estimations for the sides involving the edge of the triangle. Those are the sides of the triangle and the base.  

The mistake in the thinking is that there are 3 sets of harmonious sides where in actuality there should just be 2.

What your friend isn't considering is the proportion of the base points.  

Realizing that two comparing sides are compatible is useful. Be that as it may, in light of the fact that two of the sides are compatible doesn't make the third relating side consistent.  

This is on the grounds that the length of the side will shift contingent upon the proportion of the point it makes with different sides. As the edge changes, the length of the side will change too.