Theorem: If two sides of a triangle are unequal, the longer side has greater angle opposite to it. Given: A in which To Prove: Construction: Mark a point D on AC such that AB = AD. Join BD. Proof: In we have AB = AD [By construction] [ Angles opp. to equal sides are equal] ...(i) |
Now, consider . We find that is the exterior angle of and an exterior angle is always greater than interior opposite angle. Therefore,
[] ....(ii)
From (i) and (ii), we have
.....(iii)
But, is a part of
.....(iv)
From (iii) and (iv), we get
Hence Proved
In the above figure, find the longest side. | |||
Right Option : C | |||
View Explanation |
In the following figure , PQ > PR. QS and RS are the bisectors of respectively. Find the relation between SQ and SR. | |||
Right Option : C | |||
View Explanation |
In a triangle ABC, , and . Then which side will be of greater length? | |||
Right Option : B | |||
View Explanation |
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