Given: AC bisects angle BCD , Angle ABC is congruent to angle ADC prove AB is congruent to AD. Help immediately

Question

Given: AC bisects angle BCD , Angle ABC is congruent to angle ADC prove AB is congruent to AD. Help immediately

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Amity 4 years 2021-08-11T18:02:54+00:00 2 Answers 7 views 0

Answers ( )

  1. Helga
    0
    2021-08-11T18:04:35+00:00
    Reply

    Answer:

    Solution given;

    <BCA=<ACD

    <ABC=<ADC

    now

    In traingle ABC & ∆ ACD

    AC=AC[common base]

    <BCA=<ACD[bisector bisect it]

    <ABC=<ADC[Given]

    ∆ABC is congruent to ∆ ACD by S.A.A. axiom

    AB is congruent to AD.

    [ corresponding sides of a congruent triangle are equal]

    Hence proved.

  2. thienan
    0
    2021-08-11T18:04:47+00:00
    Reply

    AC bisects ∠BAD, => ∠BAC=∠CAD ….. (1)

    thus in ΔABC and ΔADC,    ∠ABC=∠ADC (given),

                                          ∠BAC=∠CAD      [from (1)],

    AC (opposite side side of ∠ABC) = AC (opposite side side of ∠ADC), the common side between ΔABC and ΔADC

    Hence,      by AAS axiom, ΔABC ≅ ΔADC,

    Therefore,  BC (opposite side side of ∠BAC) = DC (opposite side side of ∠CAD),  since (1)

    Hence, BC=DC proved.

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