prove that the angle opposite to equal sides of an isosceles triangle are equal .
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statement - Angles opposite to equal sides of an triangle are equal.
Given- In a triangle ABC
AB=AC
To Prove- angleB = angle C
construction- contruct AD the angle bisector of
<BAC
Proof-In triangle ABD and ACD
<BAD = <CAD ( by contruct )
AB = AC (Given )
AD = AD ( Common )
angle ABD congurent to angle ACD
( By SAS rule )
< ABD = < ACD ( corresponding
angle of congruent rule )
< ABC = < ACB
AB = AC
Hence it is proved that AB =AC
Hope this will help you
Given- In a triangle ABC
AB=AC
To Prove- angleB = angle C
construction- contruct AD the angle bisector of
<BAC
Proof-In triangle ABD and ACD
<BAD = <CAD ( by contruct )
AB = AC (Given )
AD = AD ( Common )
angle ABD congurent to angle ACD
( By SAS rule )
< ABD = < ACD ( corresponding
angle of congruent rule )
< ABC = < ACB
AB = AC
Hence it is proved that AB =AC
Hope this will help you
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