Question

Among the following, identify the pair of triangles that are NOT similar.

• A.

  

• B.

  

• C.

  

• D.

  

Hint:

For similarity of triangles, always check if corresponding angles are equal and sides are proportional.

Answer 1

The Correct Option is C

We know that for two triangles to be similar, the following conditions must hold:
1. Corresponding angles of the two triangles must be equal.
2. The sides of the triangles must be proportional.
Let us analyze each option: Option (1):
Triangle \( \triangle ABC \) and triangle \( \triangle PQR \) have angles \( 70^\circ, 60^\circ \) and \( 70^\circ, 50^\circ \) respectively.
The corresponding angles of both triangles are equal, and hence, they are similar. Option (2):
Triangle \( \triangle ABC \) has sides \( 6 \), \( 5 \), and \( 4 \), and triangle \( \triangle PQR \) has sides \( 4.5 \), \( 6 \), and \( 4.5 \).
Since the ratios of corresponding sides are not equal, these triangles are not similar. Option (3):
Triangle \( \triangle ABC \) and triangle \( \triangle PQR \) have angles \( 90^\circ, 60^\circ \) and \( 90^\circ, 80^\circ \), respectively.
The corresponding angles are not equal, hence these triangles are not similar. Option (4):
Triangle \( \triangle ABC \) and triangle \( \triangle PQR \) both have angles \( 60^\circ, 60^\circ \), and the third angle in both triangles is \( 60^\circ \).
Since the angles are equal, the triangles are similar. Thus, the pair of triangles that are not similar is option (3).