In a trapezium A B C D- if A B C D- then A C2-B D2- -a B C2-A D2-2 B C - A Db A B2-C D2-2 A B - C Dc A B2-C D2-2 A D - B Cd B C2-A D2-2 A B - C D

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Parallelogram

In a trapeziu...

Question

In a trapezium ABCD, if AB || CD, then (AC² + BD²) = ?
(a) BC² + AD² + 2BC ⋅ AD
(b) AB² + CD²+ 2AB ⋅ CD
(c) AB² + CD² + 2AD ⋅ BC
(d) BC² + AD² + 2AB ⋅ CD

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Solution

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

(a) $B C^{2} + A D^{2} + 2 B C . A D$

(b) $A B^{2} + C D^{2} + 2 A B . C D$

(d) $B C^{2} + A D^{2} + 2 A B . C D$

A B C D

A C^{2} + B D^{2} = A B^{2} + B C^{2} + C D^{2} + D A^{2}

If $A B C D$ is a rhombus then prove that ${A B}^{2} + {B C}^{2} + {C D}^{2} + {D A}^{2} = {A C}^{2} + {B D}^{2}$ .

A B C D ∠ B = 90^{o}

A D^{2} = A B^{2} + B C^{2} + C D^{2}

∠ A C D = 90^{o}

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