Question

To construct a triangle, given its perimeter and its two base
angles.​

Answer 1

Answer:

Given: The Perimeter (AB + BC + CA) of the triangle and two angles (i.e. ∠B and ∠C).

Requirements: A ruler, a protractor and a compass.

Steps of Construction:

Step 1: Draw a line segment XY such that XY = AB + BC + CA (i.e. perimeter of triangle ABC) and draw the angle lines at X and Y such that ∠LXY = ∠B and ∠MYX = ∠C.

Step 2: Draw the angle bisectors of ∠LXY and ∠MYX and let them meet at A.

Step 3: Now, draw the perpendicular bisectors of AX and AY such that they intersect XY at B and C respectively. Join AB and AC.

Hence, this is the required triangle ABC.