In a given figure AD=BD=CD.Then prove that BAC is right angle.
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In the figure, AD = BD (Given)
Therefore, angle DAB = angle DBA = x (Say)
Also, CD = AD (Given)
Therefore, angle DCA = angle DAC = y (Say)
From angle sum property, angle DBA + angle DCA + angle CAB = 180 deg.
But angle CAB = angle DAB + angle DAC
angle DBA + angle DCA + angle DAB + angle DAC = 180 deg.
Therefore x + y + x + y =180 deg.
2 (x+y) = 180 deg.
x+y = 90 deg.
But x+y = angle DAB + angle DAC = angle CAB = 90 deg.
Therefore triangle ABC is a right angle triangle.
Therefore, angle DAB = angle DBA = x (Say)
Also, CD = AD (Given)
Therefore, angle DCA = angle DAC = y (Say)
From angle sum property, angle DBA + angle DCA + angle CAB = 180 deg.
But angle CAB = angle DAB + angle DAC
angle DBA + angle DCA + angle DAB + angle DAC = 180 deg.
Therefore x + y + x + y =180 deg.
2 (x+y) = 180 deg.
x+y = 90 deg.
But x+y = angle DAB + angle DAC = angle CAB = 90 deg.
Therefore triangle ABC is a right angle triangle.
LakshaySharma11:
We need to prove angle BAC right angle...not the whole ∆
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16
hope it will help you
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