prove that the angles, opposite to the equal sides of a triangle are equal
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iven: A triangle ABC in which AB = AC
To Prove: ∠ABC = ∠ACB
Construction: Draw the bisector AD of A so as to intersect BC at D.
Proof: In ∆ADB and ∆ADC,
AD = AD | Common
AB = AC | Given
∠BAD = ∠CAD
| By Construction
∴ ∆ADB ≅ ∆ADC
| SAS congruence rule
∴ ∠ABD = ∠ACD | CPCT
⇒ ∠ABC = ∠ACB
To Prove: ∠ABC = ∠ACB
Construction: Draw the bisector AD of A so as to intersect BC at D.
Proof: In ∆ADB and ∆ADC,
AD = AD | Common
AB = AC | Given
∠BAD = ∠CAD
| By Construction
∴ ∆ADB ≅ ∆ADC
| SAS congruence rule
∴ ∠ABD = ∠ACD | CPCT
⇒ ∠ABC = ∠ACB
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