ABCD is a rhombus. Show that …

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ABCD is a rhombus. Show that AC bisects angle A as well as angle C and diakonals bisect angle B as well as angle D

Posted by Utkarsh Star 5 years, 11 months ago

CBSE > Class 09 > Mathematics

2 answers

Sia ? 5 years, 11 months ago

Given: ABCD is a rhombus

In $\triangle$ ABC and $\triangle$ ADC,
AB = CD [Sides of a rhombus]
BC = DA [Sides of a rhombus]
AC = AC [Common]
$\therefore$ $\triangle$ ABC $\cong$ $\triangle$ ADC [By SSS Congruency]
$\therefore$ $\angle$ CAB = $\angle$ CAD And $\angle$ ACB = $\angle$ ACD
Hence AC bisects $\angle$ A as well as $\angle$ C
Similarly, by joining B to D, we can prove that $\triangle$ ABD $\cong$ $\triangle$ CBD
Hence BD bisects $\angle$ B as well as $\angle$ D

1Thank You

Utkarsh Star 5 years, 10 months ago

Thanx

1Thank You

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