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Assertion : In DeltaABC and DeltaPQR, AB...

Assertion : In `DeltaABC and DeltaPQR, AB=PQ AC=PR and angle BAC= angle QPR`
`:. DeltaABC ~=DeltaPQR`
Reason : Both the triangles are congruent by SSS congruence.

A

If both assertion and reason are true and reason is the correct explanation of assertion.

B

If both assertion and reason are true but reason is not the correct explanation of assertion.

C

If assertion is true but reason is false.

D

If assertion is false but reason is true.

Text Solution

AI Generated Solution

The correct Answer is:
To solve this question, we need to analyze the assertion and the reason provided regarding the triangles \( \Delta ABC \) and \( \Delta PQR \). ### Step-by-Step Solution: 1. **Identify the Given Information**: - We have two triangles: \( \Delta ABC \) and \( \Delta PQR \). - The following conditions are given: - \( AB = PQ \) - \( AC = PR \) - \( \angle BAC = \angle QPR \) 2. **Understanding the Assertion**: - The assertion states that \( \Delta ABC \sim \Delta PQR \) (meaning the triangles are similar). - Similar triangles have proportional sides and equal corresponding angles. 3. **Understanding the Reason**: - The reason states that both triangles are congruent by SSS (Side-Side-Side) congruence. - For SSS congruence to hold, all three sides of one triangle must be equal to the three sides of the other triangle. 4. **Analyzing the Congruence**: - We have two sides \( AB \) and \( AC \) from triangle \( ABC \) that correspond to \( PQ \) and \( PR \) from triangle \( PQR \), respectively. - However, we do not have information about the third side \( BC \) and \( QR \). Therefore, we cannot conclude that \( BC = QR \). 5. **Applying the SAS Congruence**: - We can apply the Side-Angle-Side (SAS) congruence criterion: - Since \( AB = PQ \), \( AC = PR \), and \( \angle BAC = \angle QPR \), we can conclude that \( \Delta ABC \) is congruent to \( \Delta PQR \) by SAS congruence. 6. **Conclusion**: - The assertion is true because the triangles are indeed similar (and can also be proven congruent using SAS). - The reason provided (SSS congruence) is false because we do not have enough information about the third sides \( BC \) and \( QR \). ### Final Answer: - The assertion is true, but the reason is false. Therefore, the correct option is that the assertion is true, but the reason is false.
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