Question

In the figure, there is a pair of similar triangles. Its correct symbolic expression will be 

• A. \(\triangle ABC \sim \triangle DEF\)
• B. \(\triangle ABC \sim \triangle EFD\)
• C. \(\triangle ABC \sim \triangle EDF\)
• D. All of these

Hint:

Two triangles are similar if two corresponding sides are in proportion and the included angle is equal (SAS similarity).

Answer 1

The Correct Option is C

Step 1: Compare triangles.
In both triangles, the given angles are equal: \(80^\circ\) in \(\triangle ABC\) and \(80^\circ\) in \(\triangle DEF\).
Step 2: Check corresponding sides.
\[ \frac{AB}{DE} = \frac{2.5}{5} = \frac{1}{2}, \quad \frac{BC}{EF} = \frac{3}{6} = \frac{1}{2} \] Thus, the sides are proportional, and one angle is equal.
Step 3: Apply the SAS similarity criterion.
Hence, \(\triangle ABC \sim \triangle EDF\).
Step 4: Conclusion.
The correct symbolic relation is \(\triangle ABC \sim \triangle EDF\).