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ABCD is a rhombus show that …

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ABCD is a rhombus show that diagonal AC bisects angleA as well as angleC and diagonal BD bisects angleB as well as angleD

    • Posted by Jagan Mann 2 years, 8 months ago

    CBSE > Class 09 > Mathematics
    • 1 answers

    Preeti Dabral 2 years, 8 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

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