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, 5 months ago

CBSE > Class 09 > Mathematics

2 answers

Sia ? 5 years, 5 months ago

Given: ABCD is a rhombus

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

1Thank You

Utkarsh Star 5 years, 4 months ago

Thanx

1Thank You

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CBSE > Class 09 > Mathematics