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ABC and AMP are two right …

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ABC and AMP are two right triangles, right angled at B and M respectively. Prove that 1-ΔABC.~ΔAMP. 2- CA/PA = BC/MP.

    • Posted by Ruthi Lalawmpuii 6 years, 6 months ago

    CBSE > Class 10 > Mathematics
    • 1 answers

    Sia ? 6 years, 6 months ago

    Given: In the figure, ABC and AMP are two right triangles, right angled at B and M respectively,

    To prove:

    1. {tex}\triangle {/tex}ABC {tex} \sim {/tex} {tex}\triangle {/tex}AMP
    2. {tex}\frac{{CA}}{{PA}} = \frac{{BC}}{{MP}}{/tex}

    Proof:

    1. In {tex}\triangle {/tex}ABC {tex} \sim {/tex} {tex}\triangle {/tex}AMP
      {tex}\angle{/tex}ABC = {tex}\angle{/tex}AMP (1) ........ [Each equal to 90o]
      {tex}\angle{/tex}BAC={tex}\angle{/tex}MAP (2).........[Common angle]
      In view of (1) and (2)
      {tex}\triangle {/tex}ABC {tex} \sim {/tex} {tex}\triangle {/tex}AMP ..........AA similarity criterion
    2. {tex}\triangle {/tex}ABC {tex} \sim {/tex} {tex}\triangle {/tex}AMP.........Proved above in(i)
      {tex}\therefore {/tex} {tex}\frac{{CA}}{{PA}} = \frac{{BC}}{{MP}}{/tex}.........Corresponding sides of two similar triangles are proportional.

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