    Question

# Rahul was trying to make a paper toy and started with folding an A4 sized paper along the diagonal. He then noticed that there were two triangles formed. Arjun was saying that the two triangles formed are congruent to each other. But then Rahul noticed that they aren’t superimposing on each other, he says that the triangles aren’t congruent. What are the conditions for a triangle to be congruent?

A

Orientation of triangles does matter

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B

Corresponding sides should be equal

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C

Corresponding angles should be equal

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D

Orientation of triangles does not matter

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Solution

## The correct options are B Corresponding sides should be equal C Corresponding angles should be equal D Orientation of triangles does not matter AB is the diagonal of the A4 sheet. AC, BD are the lengths and AD, BC are the breadths of the A4 sheet. Consider ΔADB and ΔACB, AD = BC (Breadth of the A4 sheet) AC = BD (Length of the A4 sheet) AB is the common side for both the triangle. Therefore, ΔADB and ΔBCA are congruent under SSS congruence criterion. So, if we flip one of the triangles according to the other triangle’s orientation, it superimposes on the other. Hence, orientation is not important but the corresponding sides and angles are. There should be at least one orientation in which both the triangles superimpose on each other.  Suggest Corrections  0      Related Videos   Congruent Triangles
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