Required: To construct equilateral triangle ABC whose altitude is 6 cm.
Analysis: Draw a rough diagram of equilateral triangle ABC . Draw altitude AD on BC such that AD=6 cm. Since triangle ABC is equilateral , therefore, each angle is 60 degrees
angle A= angle B=angle C=60 degrees . AD is the altitude.
So, angle ADC= angle ADB=90 degrees.
In triangle ADC, we have angle ADC=90 degrees and angle ACD=60 degrees & angle DAC=30 degrees , angle DAB=30 degrees.
Steps of construction:
1. Draw a line PQ
2. Mark a point D and at D draw an altitude DR.
3. Cut off DA=6 cm from DR.
4. Draw angle DAC=30 degrees which meets PQ at C.
5. Mark a point B on QP such that AC=CB
6. Join AB. Hence, triangle ABC is the required triangle .