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CBSE Class 9 Answered

diagonal AC of a parallelogram ABCD bisects ∆A . i . it biseets ∆C also ii . ABCD is a rhombus
Asked by sanskritiraghudev | 19 Feb, 2022, 09:38: AM
answered-by-expert Expert Answer
To prove: (i) AC bisects angle C  (ii) ABCD is a parallelogram
left parenthesis straight i right parenthesis In space increment ADC space and space increment CBA comma AD space equals space CB space space space... space left parenthesis Opp space sides space of space straight a space llgram right parenthesis DC space equals space BA space space space... space left parenthesis Opp space sides space of space straight a space llgram right parenthesis AC space equals space CA space space space... space left parenthesis Common space sides right parenthesis rightwards double arrow increment ADC approximately equal to increment CBA space space space space... space left parenthesis By space SSS space congruence space rule right parenthesis rightwards double arrow angle ACD equals angle CAB space space space... space left parenthesis straight A right parenthesis space CPCT rightwards double arrow angle BCA equals angle CAD space space space... space left parenthesis straight B right parenthesis space CPCT rightwards double arrow angle CAB equals angle CAD space space space... space left parenthesis straight C right parenthesis space space space space space Given Thus comma space angle ACD equals angle BCA Hence comma space AC space bisects space angle straight C. left parenthesis ii right parenthesis space space angle ACD equals angle CAD AD space equals space CD space space.... space left parenthesis Sides space opposite space to space equal space angles space are space equal right parenthesis But comma space AB equals CD space & space AD equals BC space space... space left parenthesis Opp space sides space of space llgram right parenthesis AB equals BC equals CD equals DA Hence comma space ABCD space is space straight a space rhombus
Answered by Renu Varma | 24 Feb, 2022, 11:15: AM

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