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step-by-step
ABC is a triangle with AB=AC.
D is a Mid-point of BC.
prove that angle ADB Is a right angle.
as congruence
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Step-by-step explanation:
I am writing just the explanation. Draw the figure on your own.
ABC is a traingle.
In ABD and ACD,
AB = BC (given)
BD = CD (D is midpoint of BC)
AD = AD(common)
Therefore,
ABD is congruent to ACD
(by SAS congruency)
Therefore,
angle ADB = angle ADC (by CPCT)
Let angle ADB = angle ADC = x
angle ADB + angle ADC = 180°
(Linear pair)
x + x = 180°
2x = 180°
x = 90°
Therefore,
angle ADB = angle ADC = 90°
Triangle ADB is a traingle with one angle 90°. Therefore, it is a right angled traingle.
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