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If diagonals of parallelogram are equal,show …

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If diagonals of parallelogram are equal,show it is a rectangle

Posted by Shekhar Zurange 8 years, 3 months ago

CBSE > Class 09 > Mathematics

1 answers

Hans Raj 8 years, 3 months ago

let us take parallelogram ABCD

AC and BD are two diagonal which are also equal AC = BD

ABCD is a parallelogram , therefore opposite sides are equal AB = CD , AD = BC , Sum of opposite angles = 180^o , L B + L D = 180^O , LA + LC = 180^O

ABC = ADC are congruent (as AB = CD , AD = BC , AC = AC )

similarly BCD = BAD are congruent as BD=BD is common

L B = L D But LB + L D = 180 therefore LB = 90 , LD = 90 , LA = 90 and L C= 90

Hence ABCD is a rectangle

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