∆ABC is an isosceles triangle with AB =AC. AM is the bisector of angl.BAC. prove that ∆ABC =∆ACM.
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Step-by-step explanation:
When AD is the angle bisector of <BAC
ABC is an isosceles triangle in which AB = AC and AD is the bisector of <BAC.
In triangles ABD and ACD
<B = <C
AB = AC
AD is common.
Therefore triangles ABD and ACD are congruent, and so
<ADB = <ADC = 90 degrees because BCD is a straight line and = 180 degrees.
QED.
Method 2:
When AD is the bisector of BC
ABC is an isosceles triangle in which AB = AC and AD is the bisector of BC.
In triangles ABD and ACD
<B = <C
AB = AC
BD = CD.
Therefore triangles ABD and ACD are congruent, and so
<ADB = <ADC = 90 degrees because BCD is a straight line and = 180 degrees.
QED.
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