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On a common hypotenuse AB , …

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On a common hypotenuse AB , two right triangles are formed ACB and ADB are situated on oppsite sides . Prove that angle BAC = angle BDC

Posted by Shashant Ahuja 8 years, 10 months ago

CBSE > Class 09 > Mathematics

1 answers

Shweta Gulati 8 years, 10 months ago

Since they are right triangles, it is a cyclic quadrilateral and the circle with diameter AB passes through all 4 points. Since ∠BAC and ∠BDC both subtend the same arc, BC, of this circle, and since the vertices of these angles are both on the circle, the two angles are equal by the theorem that says all angles subtending the same arc with vertices on the circle are equal.

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CBSE > Class 09 > Mathematics