Question

If in $\triangle ABC$ and $\triangle DEF$, $\dfrac{AB}{DE} = \dfrac{BC}{FD}$, then they will be similar if

• A. $\angle B = \angle E$
• B. $\angle A = \angle F$
• C. $\angle A = \angle D$
• D. $\angle B = \angle D$

Hint:

For SAS similarity, the included angle between the two proportional sides must be equal.

Answer 1

The Correct Option is C

Step 1: Recall the condition for similarity of triangles.
If two sides of one triangle are in proportion to two sides of another triangle, and the included angle is equal, then the triangles are similar (SAS similarity criterion).
Step 2: Identify included angles.
In $\triangle ABC$ and $\triangle DEF$, if $\dfrac{AB}{DE} = \dfrac{BC}{FD}$, then the included angles are $\angle A$ and $\angle D$.
Step 3: Apply SAS similarity condition.
For the triangles to be similar, $\angle A = \angle D$ must hold true.

Step 4: Conclusion.
Hence, $\triangle ABC \sim \triangle DEF$ when $\angle A = \angle D$.