In triangles ABC and PQR, AB = AC, ∠C = ∠P and ∠B = ∠Q. Then the two triangles ________.

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RRB Group D Previous Year Paper (Held on: 26 Aug 2022 Shift 2)
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  1. are isosceles and congruent.
  2. are neither congruent, nor isosceles.
  3. are congruent but not isosceles.
  4. are isosceles but not congruent.

Answer (Detailed Solution Below)

Option 4 : are isosceles but not congruent.
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Detailed Solution

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Given:

Triangles ABC and PQR

AB = AC

∠C = ∠P

∠B = ∠Q

Formula used:

For two triangles to be congruent by ASA (Angle-Side-Angle) criterion, two angles and the included side must be equal.

Calculation:

Since AB = AC, ∠C = ∠P, and ∠B = ∠Q, both triangles are isosceles.

However, we do not have information about the length of sides or the exact measures of the angles to conclude congruence.

∴ The correct answer is option (4).

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