Question

Construct a triangle ABC whose perimeter 12 cm and whose base angles are 65° and 85°.

Answer 1

Steps of construction:

Step I: Draw line segment PQ = 12 cm (AB + BC + CA = 12 cm)

Step II: Construct ∠RPQ of measure 65° at point P and ∠PQS of measure 85° at point Q.

Step III: Bisect ∠RPQ and ∠PQS. Let these bisectors intersect each other at point A.

Step IV: Draw perpendicular bisectors UV of AP and WX of QA.

Step V: Let UV intersect PQ at B and WX intersect PQ at C. Join AB and AC

ΔABC is the required triangle.