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Diagonal AC of a parallelogram ABCD bisects ∠A (see Fig. 8.19). Show that (i) it bisects ∠C also,Q.6 (1)

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Please guide me the best way for solving the question of class 9th math of Quadrilaterals chapter of exercise 8.1of math of question no. 6 What is the best way for solving this question, please guide me Diagonal AC of a parallelogram ABCD bisects ∠A (see Fig. 8.19). Show that (i) it bisects ∠C also,

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  1. (i) In ΔADC and ΔCBA,

    AD = CB (Opposite sides of a parallelogram)

    DC = BA (Opposite sides of a parallelogram)

    AC = CA (Common Side)

    , ΔADC ≅ ΔCBA [SSS congruency]

    Thus,

    ∠ACD = ∠CAB by CPCT

    and ∠CAB = ∠CAD (Given)

    ⇒ ∠ACD = ∠BCA

    Thus,

    AC bisects ∠C also.

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