NCERT Exemplar Solutions
Class 6 - Mathematics - Unit 2: Geometry - Multiple Choice Questions
Question 16

Question.  16

In Fig. 2.13, PQ ⟂ RQ, PQ = 5 cm and QR = 5 cm. Then \(\triangle PQR\) is

(A)

a right triangle but not isosceles

(B)

an isosceles right triangle

(C)

isosceles but not a right triangle

(D)

neither isosceles nor right triangle

Detailed Answer with Explanation:

  1. PQ ⟂ RQ means the angle at Q is a right angle.
    Write it: \(\angle Q = 90^\circ\).
  2. Given side lengths: \(PQ = 5\,\text{cm}\) and \(QR = 5\,\text{cm}\).
    So the two sides meeting at Q are equal: \(PQ = QR\).
  3. Definition check:
    Right triangle ⟺ it has one \(90^\circ\) angle.
    Isosceles triangle ⟺ it has two equal sides.
  4. Here both conditions hold:
    \(\angle Q = 90^\circ\).
    \(PQ = QR\).
  5. Therefore the triangle is both right and isosceles.
    So \(\triangle PQR\) is an isosceles right triangle.
    Answer: Option B.
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