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In a figure if angle x …

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In a figure if angle x = angle y and ab = cb prove that ae = cd

    • Posted by Kamiya Shah 4 years, 3 months ago

    CBSE > Class 09 > Mathematics
    • 1 answers

    Sia ? 4 years, 3 months ago

    Consider the triangles AEB and CDB
    {tex}\angle{/tex}EBA = {tex}\angle{/tex}DBC ... (Common angle)  ... (i)
    Further, we have:
    {tex}\angle{/tex}BEA = 180 - y
    {tex}\angle{/tex}BDC = 180 - x
    Since x = y, we have:
    180 - x = 180 - y
    {tex}\angle{/tex}BEA = {tex}\angle{/tex}BDC ... (ii)
    AB = CB ... (Given) ... (iii)
    From (i), (ii) and (iii), we have:
    {tex}\triangle{/tex}BDC{tex}\cong{/tex}{tex}\triangle{/tex}BEA ... (AAS criterion)
    {tex}\therefore{/tex} AE = CD (CPCT)
    Hence, proved.

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