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Congruence of Triangles

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In Fig 7.28, ray AZ bisects angle DAB as well as angle DCB.

5. In Fig 7.28, ray AZ bisects $\angle DAB$ as well as $\angle DCB$ .

           (i) State the three pairs of equal parts in triangles $BAC$ and $DAC$ .
           (ii) Is $\Delta BAC\cong \Delta DAC ?$ Give reasons.
           (iii) Is $AB = AD ?$ Justify your answer.
           (iv) Is $CD = CB \; ?$ Give reasons.

Answers (1)

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P Pankaj Sanodiya

i)

Given in triangles $BAC$ and $DAC$

$\angle DAC=\angle BAC$

$\angle DCA=\angle BCA$

$\overline {AC}=\overline {AC}$ ( common side)

ii)

So, By ASA congruency criterion,triangles $BAC$ and $DAC$ are congruent.

$\Delta BAC\cong\Delta DAC$

iii)

Since $\Delta BAC\cong\Delta DAC$ , all corresponding parts will be equal. So

$AB = AD$ .

iv)

Since $\Delta BAC\cong\Delta DAC$ , all corresponding parts will be equal. So

$CD = CB \;$

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