2. In Fig, sides AB and AC of \small \Delta ABC are extended to points P and Q respectively. Also, \small \angle PBC < \angle QCB. Show that \small AC> AB.

             

Answers (1)

We are given that, 

                                    \small \angle PBC < \angle QCB                                                                                        ......................(i)

Also,                            \angle ABC\ +\ \angle PBC\ =\ 180^{\circ}                    (Linear pair of angles)          .....................(ii)

and                              \angle ACB\ +\ \angle QCB\ =\ 180^{\circ}                    (Linear pair of angles)          .....................(iii)

From (i), (ii) and (iii) we can say that :

                                     \angle ABC\ > \ \angle ACB

Thus   AC\ > AB   ( Sides opposite to the larger angle is larger.)

  

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