Question

Construct a triangle ABC in which BC is 5 cm, $\angle B$ is ${60}^{\circ }$ and AB + AC = 10cm. Which type of triangle is this? [3MARKS]

Answer 1

Steps : 1 Mark
Construction : 2 Marks

Steps-

1. Draw a line segment BC of length 5 cm using ruler.
2. At B construct an angle of measurement ${60}^{\circ }$ which makes an $\angle {60}^{\circ }$ with BC. Draw ray BX .
3. Cut a line segment BD equal to AB + AC = 10 cm on ray BX.
4. Join CD. Construct perpendicular bisector PQ of CD.
Let PQ intersect BD at point A.
5. Join AC.
$△ABC$ is the required triangle.

By inspection, it os observed that triangle ABC is an equilateral triangle.