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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