Question

Draw triangles of the following measurements.

(i) ΔPQR : PQ = 5 cm, ∠P = 65°, ∠Q = 65°

(ii) ΔABC : AB = 6 cm, ∠A = 40°, ∠B = 40°

(iii) ΔLMN : LM = 4 cm, ∠L = 90°, ∠M = 30°

(iv) ΔXYZ : XY = 5 cm, ∠X = 90°, ∠Q = 45°

Answer 1

(i) The steps for construction of the required triangle are as follows.

1. Draw a line segment PQ of length 5 cm.

2. Draw a line segment through point P, making an angle of 65° with PQ.

3. Draw a line segment through point Q, making an angle of 65° with PQ. Mark the point of intersection as R.

Thus, ΔPQR is the required triangle.

(ii) The steps for construction of the required triangle are as follows.

1. Draw a line segment AB of length 6 cm.

2. Draw a line segment through point A, making an angle of 40° with AB.

3. Draw a line segment through point B, making an angle of 40° with AB. Mark the point of intersection as C.

Thus, ΔABC is the required triangle.

(iii) The steps for construction of the required triangle are as follows.

1. Draw a line segment LM of length 4 cm.

2. Draw a line segment through point L, making an angle of 90° with LM.

3. Draw a line segment through point M, making an angle of 30° with LM. Mark the point of intersection as N.

Thus, ΔLMN is the required triangle.

(iv) The steps for construction of the required triangle are as follows.

1. Draw a line segment XY of length 5 cm.

2. Draw a line segment through point X, making an angle of 90° with XY.

3. Draw a line segment through point Y, making an angle of 45° with XY. Mark the point of intersection as Z.

Thus, ΔXYZ is the required triangle.