Question

ABC and ADC are two right triangles with common hypotenuse AC. Prove that ∠CAD = ∠CBD.

Answer 1

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Answer 2

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Solution:

AC is the common hypotenuse for two right triangles, ∆ABC and ∆ADC.

∠ABC=∠ADC=90°        (Given)

⇒∠ABC+∠ADC=180°

(If sum of a pair of opposite angles of a quadrilateral is 180°, the quadrilateral is cyclic.)

Therefore, quadrilateral ABCD is cyclic.

⇒∠CAD=∠CBD.    (Angles in the same segment are equal)

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