Question 4 Construct the following and give justification : An equilateral triangle, if its altitude is 3.2cm.
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Solution
We know that in an equilateral triangle all the sides are equal and all angles are equal i.e., each angle is 60∘. Given, the altitude of an equilateral triangle is 3.2cm. Steps to construct the ΔABC. (i) Draw a line PQ. (ii) Take a point D on PQ and draw a ray DE⊥PQ. (iii) Cut the line segment AD of length 3.2cm on the ray DE. (iv) Make angles ∠DAB=30∘ at A with line AB intersecting DP. (v) Cut the line segment DC on DQ such that DC = BD. (vi) Join AC, thus, ΔABCis the required triangle.