Question

Construct the following and give justification:

An equilateral triangle if its altitude is 3.2 cm.

Answer 1

Step 1: Draw a line XY.

Step 2: Mark a point D on XY and construct DZ perpendicular to XY.

Step 3: With center D and radius 3.2 cm cut an arc on DZ at A.

Step 4: With A as center, draw ∠UAD = 30° intersecting XY at B and ∠VAD = 30° intersecting XY at C.

ABC is the required triangle.

Justification:

By construction we can say,

∠ZDY = 90°

∠BAC = ∠BAD + ∠CAD

∠BAC = 30° + 30° = 60°

In ΔABD,

∠ABD + ∠BAD + ∠DBA = 180°  ...(By angle sum property)

30° + 90° + ∠DBA = 180°

∠DBA = 60°

Similary, ∠DCA = 60°

Thus, ∠A = ∠B = ∠C = 60°

Thus, our construction is justified.