Question

Construct an isosceles triangle using the given data: Altitude RM = 5cm and vertex ∠R = 120°

Answer 1

Altitude RM = 5cm and vertex ∠R = 120°

Steps of construction:
1. Draw a line SU of any length.
2. Take a point M on SU.
3. Through the point M on SU draw NM perpendicular to SU.
4. With M as centre and radius 5cm, draw an arc to cut NM at R.
5. Construct ∠MRP = ∠MRQ = `(1)/(2) xx 120°` = 60°.
(a) With R as centre, draw an arc cutting RM at L.
(b) With L as centre and same radius, cut the arc at X and Y.
(c) Join RX and RY and produce them to T and V respectively. RT and RV make an angle of 60° with Rm.
(d) Mark the points as P and Q where RT and RV meet SU.
Thus, PQR is the required triangle.