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Question
Construct a triangle PQR such that PQ = QR = 5 .5 cm and angle PQR = 90°. If possible, draw its lines of symmetry.
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Solution
∴ ∠PQR = 90°, and ∠P = ∠R ............(opposite sides are equal)
∴∠P + ∠R = 90°
Hence ZP = ZR = = 45°
Steps of Construction:
(i) Draw a line segment QR = 5.5 cm
(ii) At Q, draw a ray making an angle of 90° and cut off QP = 5.5 cm.
(iii) Join PR.
∆ PQR is an isosceles triangle.
(iv) Draw the angle bisector of ∠PQR. It is the line of symmetry. Since the triangle is an isosceles.
∴It has only one line of symmetry.
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