In the figure, ABC is a triangle in which AD is the bisector of angleA. If AD perpendicular to BC, show that ABC is isosceles.
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Step-by-step explanation:
In ∆ABD & ∆ACD,
angle BAD = angle CAD [since AD bisects angle A]
AD = AD [common side]
angle ADB = angle ADC [each90°]
Therefore ∆ABD congruent to ∆ACD
So, AB = AC [CPCT]
Therefore, ∆ABC is an isosceles ∆.
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