Question

Construct a triangle ABC in which BC is 5 cm, $\angle B$ is ${60}^{\circ }$ and AB - AC=0 cm. What type of triangle is this?

Answer 1

Steps:
1. Draw a line segment BC = 5 cm. Draw ray BX which makes an angle ${60}^{\circ }$ with BC.
2. Cut off line segment BD of length (AB - AC) on BX on the opposite side of BC.
But AB - AC is 0. Hence point B and point D are the same.
3. Draw the perpendicular bisector of BC.
Let the perpendicular bisector intersect ray BX at A.
4. Angle ABC is the required triangle.
5. By inspection it can be observed that the triangle obtained is an equilateral triangle.