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Question

In the given figure, if ADBC and BD = DC, then which of the following are true ?


A

BADCAD by ASA postulate

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B

BADCAD SAS postulate

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C

AD bisects BAC

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D

ABC is isosceles

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Solution

The correct options are
B

BADCAD SAS postulate


C

AD bisects BAC


D

ABC is isosceles


In BADCAD

(i) AD = AD ......(common)

(ii) ADB=ADC=90

(iii) BD = CD ......(given)

(iv) BADCAD ........(SAS postulate)

(v) BAD=CAD

(vi) AD bisects BAC ........(from (v))

(vii) AB = AC ....(cpct)

(viii) ABC is isosceles .....(from (vii))

Hence (B),(C) and (D)


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