Question

Construct a triangle ABC in which BC is 8 cm, Angle B is ${75}^{\circ }$ and AB + AC = 15cm by using method of perpendicular bisector. [4 MARKS]

Answer 1

Steps : 1 Mark
Construction : 3 Marks

Steps :
1. Draw line segment BC of length 8 cm using ruler.
2. At B construct an angle of measure ${75}^{\circ }$ which makes an angle ${75}^{\circ }$ with BC.Draw ray BX .
3. Cut a line segment BD equal to AB + AC = 15 cm from ray BX.
4. Join CD. Construct perpendicular bisector PQ for CD. Let PQ meet BD at A.
5. Join AC. Triangle ABC is the required triangle.