Question

In triangles ABC and PQR, \( \angle A = \angle Q \) and \( \angle B = \angle R \), then \( AB : AC \) is equal to :

• A. \( PQ : PR \)
• B. \( PQ : QR \)
• C. \( QR : QP \)
• D. \( PR : QR \)

Hint:

The order of vertices in a similarity statement is crucial. Match the equal angles to set up the correct ratio.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
By AA (Angle-Angle) similarity criterion, if two angles of one triangle are equal to two angles of another triangle, the triangles are similar.
Step 2: Detailed Explanation:
Given: \( \angle A = \angle Q \) and \( \angle B = \angle R \).
Therefore, \( \triangle ABC \sim \triangle QRP \). (Order: \( A \rightarrow Q \), \( B \rightarrow R \), \( C \rightarrow P \)).
In similar triangles, corresponding sides are in the same ratio:
\[ \frac{AB}{QR} = \frac{BC}{RP} = \frac{AC}{QP} \]
From the ratio \( \frac{AB}{QR} = \frac{AC}{QP} \), we can write:
\[ \frac{AB}{AC} = \frac{QR}{QP} \]
Step 3: Final Answer:
\( AB : AC = QR : QP \).