Question

If the two sides of a triangle are in the same proportion of the two sides of another triangle, and the angle inscribed by the two sides in both the triangles are equal in measure, then the triangles are similar to each other by the criteria -

• A. Side Angle Side
• B. Angle Angle
• C. Side Side Side
• D. None of the above.

Answer 1

The correct option is A Side Angle Side

Consider the following two triangles:


If the two sides of a triangle are in the same proportion of the two sides of another triangle, and the angle inscribed by the two sides in both the triangles are equal in measure, then the triangles are similar to each other by Side-angle-side similiarity rule.

From the figure,

$\frac{AB}{PQ}=\frac{BC}{QR}=\frac{1}{k}$
and $\angle B=\angle Q.$

So, the triangles $△ABC\sim △PQR$ by SAS property.

Hence, option $\left(a\right)$ correct.