Is the following statement always true? “If an angle of one triangle equals an angle of another and two sides of one triangle are proportional to the corresponding two sides of the other triangle, then the triangles are similar.” Give reasons.
Not always.
Let us go step by step:
Step 1: Recall the condition for SAS similarity of two triangles.
If these two conditions are satisfied, then the triangles are similar.
Step 2: In the question, we are told:
Step 3: This information is not enough unless the equal angle lies between the two proportional sides.
If the equal angle is the included angle between the two proportional sides, then the triangles will definitely be similar (by SAS similarity).
Step 4: But if the equal angle is not the included angle, then the triangles may or may not be similar. In fact, we can even draw counterexamples where similarity fails.
Final Conclusion: Therefore, the statement given in the question is not always true. It is true only when the equal angle is the included angle between the proportional sides.