50 ! which pairs of triangles can be shown to be congruent using rigid motions?

The pairs shown in 1,3, 6 are congruent and the pairs shown in 2,4,5 are not congruent.

Explanation:

From the given figure we can easily noticed that the triangles ABC, DEF and QRS can be easy formed by rigid motions because the corresponding sides are same. But the triangle JKL can not be formed by rigid motions.

The triangle DEF can be formed if triangle ABC reflects across x-axis and after that it reflects across the y-axis.

So, triangle ABC and DEF are congruent.

The  triangle QRS can be formed if triangle ABC reflects across y-axis and after that it translated by (0,-1).

So, triangle ABC and QRS are congruent.

Since the ABC and DEF are congruent, and ABC and QRS are congruent, So by using transitive property of congruent DEF and QRS are congruent.

Therefore only the pairs shown in 1,3, 6 are congruent and the pairs shown in 2,4,5 are not congruent.

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