Question

How to construct a triangle in which perimeter is 12 cm and angle b is 80 degree and angle c is 60 degree

Answer 1

Step-by-step explanation:

Given the base angles, say ∠ B and ∠ C and BC + CA + AB, you have to construct

the triangle ABC.

Steps of Construction :

1. Draw a line segment, say XY = 12 cm equal to BC + CA + AB.

2. Make angles LXY equal to ∠B and MYX equal to ∠C.

3. Bisect ∠ LXY and ∠ MYX. Let these bisectors intersect at a point A

4. Draw perpendicular bisectors PQ of AX and RS of AY.

5. Let PQ intersect XY at B and RS intersect XY at C. Join AB and AC

Then ABC is the required triangle. For the justification of the construction, you

observe that, B lies on the perpendicular bisector PQ of AX.

Therefore, XB = AB and similarly, CY = AC.

This givesBC + CA + AB = BC + XB + CY = XY.

Again∠BAX = ∠AXB (As in ∆ AXB, AB = XB) and

∠ABC = ∠BAX + ∠AXB = 2 ∠AXB = ∠LXY

Similarly,∠ACB = ∠MYX as required.