Question

(i) Given are 4 sets of triangle constructions. Identify which of these following triangles cannot be constructed. Give reasons for each of them.

1. $\angle$ A = 60${}^{\circ }$, AB= 4 cm, AC = 5 cm
2. PQ = 4 cm, QR = 5 cm, RP = 11 cm
3. D = 90${}^{\circ }$ , EF = 13 cm, DE = 5 cm
4. S = 90${}^{\circ }$, T = 120${}^{\circ }$, ST = 5 cm

(ii) Also, construct a right angled $△$ PQR, where measure of $\angle Q={90}^{\circ },$ QR = 8 cm and PR = 10 cm.

Answer 1

(i) 2 and 4 cannot be constructed.

For the 2nd one, the sum of 2 sides is less than the 3rd side. For a triangle, the sum of any 2 sides should be greater than the third side.

In the 4th one, the sum of 2 angles is more than 180${}^{\circ }$. For a triangle, the sum of all the angles should not be more than 180${}^{\circ }$

1 and 3 can be constructed.

(ii) Steps of construction:

(1) Draw QR = 8 cm.
(2) Draw m $\angle$ Q = 90${}^{\circ }$.
(3) Draw an arc with centre R and radius 10 cm to cut the perpendicular line at P.
(4) $△$ PQR is the required triangle.