Using ruler and compasses only, construct an ΔABC, given base BC = 7 cm, ∠ABC = 60° and AB+AC=12 cm.
We are asked to construct a triangle ABC in which BC = 7 cm, B = 60° and
AB + AC = 12 cm
We will follow the following algorithm for the construction
Steps of construction
STEP1: Draw BC of length 7 cm.
STEP2: With B as a centre, and convenient radius draw an arc cutting BC at N.
STEP3: With N as a centre, and same radius draw an arc cutting the previous arc at M.
STEP4: Draw BM and produce it to P.
STEP5: From BP, cut BR = 12 cm.
STEP6: Draw segment RC.
STEP7: Draw perpendicular bisector of RC. It cuts the ray BR at A.
STEP8: Draw AC.
ABC is the required triangle.