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Question

Construct a triangle with 3 cm base and sum of other two sides is 8 cm and one base angle is 60o.

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Solution

Given the base BC of the triangle ABC be 3 cm, one base angle ∠B=60o and the sum of the other two sides be 8 cm i.e, AB + AC = 8 cm. STEPS : (i) Draw BC = 3 cm (ii) At point B, draw PB so that ∠PBC=60o (iii) From BP, cut BC = 8 cm. (iv) Join D and C. (v) Draw perpendicular bisector of CD, which meets BD at point A. (vi) Join A and C. Thus, ABC is the required triangle. Proof : Since, OA is perpendicular bisector of CD ⇒OC = OD ⇒∠AOC = ⇒∠AOD = 90° Also, OA = OA [Common] ∴△AOC ≅△ AOD [By SAS] ⇒ AC = AD ∴ BD = BA + AD = BA + AC = Given sum of the other two sides Thus, base BC and ∠B are draw as given and BD = AC. Hence Proved

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