Question

are these scalene triangles similar?

Explanation:

Step1: Calculate the ratio of corresponding sides

For the two triangles, we have two pairs of corresponding sides. Let's calculate the ratios:

• For the first pair of sides: $\frac{54}{36}=\frac{3}{2}$
• For the second pair of sides: $\frac{42}{28}=\frac{3}{2}$

Step2: Check the included - angle condition

The included angles (the angles between the pairs of corresponding sides) are equal (both are marked as congruent in the figure). According to the Side - Angle - Side (SAS) similarity criterion, if the ratios of two pairs of corresponding sides of two triangles are equal and the included angles are congruent, then the two triangles are similar.

Answer:

Yes, the two triangles are similar.