Question

Construct a triangle XYZ whose perimeter 15 cm and whose base angles are 60° and 70°.

Answer 1

Steps of construction:

Step I: Draw line segment AB = 15 cm (XY + YZ + ZX = 15 cm)

Step II: Construct ∠PAB of measure 60° at point A and ∠QBA of measure 70° at point B.

Step III: Bisect ∠PAB and ∠QBA. Let these bisectors intersect each other at point X.

Step IV: Draw perpendicular bisectors ST of AX and UV of BX.

Step V: Let ST intersect AB at Y and UV intersect AB at Z. Join XY and XZ

ΔXYZ is the required triangle.