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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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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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