Question

Rahul is trying to make a paper toy and started with folding an A4 sized paper along the diagonal. He then noticed that there are two triangles formed. Arjun is saying that the two triangles formed are congruent to each other. But as Rahul is seeing that they aren’t superimposing on each other, he says that the triangles aren’t congruent.

What are the conditions for triangles to be congruent?

• A. Orientation of triangles does matter
• B. Corresponding sides should be equal
• C. Corresponding angles should be equal
• D. Orientation of triangles does not matter

Answer 1

Answer: (B), (C), (D)

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 $AD,BC$ is the breadths of the A4 sheet.

Consider $\Delta ADB$ and $\Delta ACB,$

$AD=BC$ [Breadths of the A4 sheet]

$AC=BD$ [Lengths of the A4 sheet]

$AB$ is the common side for both the triangles.

Therefore, $\Delta ADB$ and $\Delta BCA$ 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.