Question

construct an equilateral triangle if its altitude is 6cm. give justification to your answer its for 4marks

Answer 1

1. plot a vertical line of height 6 cm. mark the top vertex as a and bottom vertex as b.
2. now, using a protractor, draw two lines making 30 degree angle to the either side of the line AB.(the altitude of the equilateral triangle acts as it's angular bisector and the internal angle of an equilateral triangle is 60 degrees.)
3. draw a line perpendicular to the vertex b using a set square.This perpendicular line meets the angular projections with equal distances.(this is because the altitude of the equilateral triangle is it's median too) let those points of concurrency be called c,d.
4. The triangle ACD formed is the required triangle.