Question

in the adjacent figure sides ab and ac of triangle ABC are extended to the points p and q also angle pbc is less than angle q c b show that AC is greater than a b

Answer 1

Proof: It is given that angle PBC is less than angle QCB.
Now angle PBC +angle ABC = 180 (linear pair)

Since angle PBC is less therefore the remaining part will be greater such that angle abc is greater.

Similarly,

angle QCB + angle ACB = 180

Angle QCB is greater therefore the remaining part will be smaller such that angle ACB is less

Therefore side AC is greater than side AB ( side opposite to greater angle is greater)

and therefore it is proved

Answer 2

Answer:

Same as above

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