Question

Construct a triangle PQR such that PQ = QR = 5 .5 cm and angle PQR = 90°. If possible, draw its lines of symmetry.

Answer 1

∴ ∠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.