Question

Identify the triangle that is similar to the triangle AOB, given same colored angles are of equal measure.

• A.
• B.
• C.

Answer 1

The correct option is C

We know that, two triangles are similar only when,
(i) All the corresponding angles are equal.
(ii) The corresponding sides are in equal proportion.

In triangle AOB and triangle EOD
$\angle BAO=\angle DEO$
$\angle OBA=\angle ODE$
$\angle AOB=\angle EOD$
So, by AAA criteria, the triangles are similar.

In triangle AOD and triangle BOC,
no two angles are equal to corresponding two angles of triangle AOB, so they are not similar to triangle AOB.