Q. 43.6( 11 Votes )

In an isosceles triangle ABC, AB = AC and P is any point on produced side BC. PQ and PR are perpendicular on sides AB and AC from the point P respectively. BS is perpendicular on side AC from point B; let’s prove that PQ – PR = BS.

Answer :

Given.


AB= AC;


PQ and PR are perpendicular on sides AB and AC from the point P respectively. BS is perpendicular on side AC from point B


Formula used.


Area of triangle = × Base × Height



As triangle ABC and triangle ACP combines to form triangle ABP


Area of triangle ABP = Area of triangle ABC + Area of triangle ACP


Area of triangle ABP = × Base × Height


× AB × PQ


Area of triangle ABC = × Base × Height


× AC × BS


Area of triangle ACP = × Base × Height


× AC × PR


× AB × PQ = × AC × BS + × AC × PR


As AB = AC (Given)


× AC × PQ = × AC × BS + × AC × PR


Taking common ×AC get removed


PQ = BS + PR


PQ – PR = BS


Hence proved;


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