construct an equilateral triangle given only its altitudeSol

construct an equilateral triangle given only its altitude

Solution

Step 1: Draw line PQ.
Step 2: Draw a perpendicular to PQ from any point on it, say D. Let this be DX.
Step 3: With D as the center and radius equal to altitude length, draw an arc cutting ray DX at A.
Step 4: Draw angle DAY = 30 , with ray AY cutting PQ at point B.
Step 5: With B as the center and radius equal to AB, draw an arc cutting line PQ at point C.
Step 6: Join points A and C.
ABC is the required triangle.