Question

ABCD is a parallelogram if the two diagonals are equal find the measure of angle abc

Answer 1

AnswEr:

Since ABCD is a parallelogram. Therefore,

→$\qquad\tt{AB=CD\:and\:\:AD=BC}$

Thus, in ∆s ABD and ACB, we have

• AD = BC⠀⠀⠀⠀⠀⠀⠀⠀⠀ [As approved above]
• BD = AC⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ [Given]
• AB = AB⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ [common]

_________________________

So, by SSS criterion of congruence, we have

• ∆ABD $\cong$ ∆ ACB

$\implies$ $\angle$BAD=$\angle$ABC

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Now, AD || BC and transversal AB intersects them at A and B respectively.

$\therefore$ $\angle$ BAD+$\angle$ ABC = 180° $\qquad\sf{[Sum\:of\:the\:interior\:angles\:on\:the\:same}$$\qquad\sf{side\:of\:a\: transversal\:is\:180\degree]}$

$\implies$ $\angle$ BAD + $\angle$ ABC = 180°

$\implies$ 2 $\angle$ ABC = 180°

$\implies$ $\angle$ ABC = 90°

Hence, the measure of $\angle$ ABC is 90°

#BAL

#Answerwithquality

Answer 2

Answer:

measure of ∆ABC is 90°

Hence proved