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ABC is an isosceles triangle in which A...

ABC is an isosceles triangle in which `A B =A C`. AD bisects exterior angle PAC and `C D ||A B`. Show that(i) `/_D A C =/_B C A ` and (ii) ABCD is a parallelogram.

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ABC is a isosceles triangle
`/_ABC=/_ACB`
1)`/_DAC=/_BCA`
`/_PAC=/_ACB+/_ABC`
`/_PAC=theta+theta=2theta`
2)ABCD is a parallelogram.
AD||AC
CD||AB.
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Knowledge Check

  • In a Delta ABC , the sum of exterior angles at B and C is equal to:

    A
    `180^(@) - angle BAC`
    B
    `180^(@) + angle BAC`
    C
    `180^(@) - 2 angle BAC`
    D
    `180^(@) + 2 angle BAC`

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