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Pythagoras Theorem

If ABC is an ...

Question

If ABC is an isosceles triangle and D is a point of BC such that AD ⊥ BC, then

(a) AB² − AD² = BD.DC
(b) AB² − AD² = BD² − DC²
(c) AB² + AD² = BD.DC
(d) AB² + AD² = BD² − DC²

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Solution

Given: ΔABC is an isosceles triangle, D is a point on BC such that

We know that in an isosceles triangle the perpendicular from the vertex bisects the base.

∴ BD = DC

Applying Pythagoras theorem in ΔABD

Since

Hence correct answer is .

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In a trapezium ABCD, if AB || CD then $(A C^{2} + B D^{2})$ = ?

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