Abc And Adc Are Two Right Triangles With Common Hypotenuse Ac Prove That Angle Cad Angle Cab

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Answers:

Given,
AC is the common hypotenuse. ∠B = ∠D = 90°.
To prove,
∠CAD = ∠CBD
 
Proof:
Since, ∠ABC and ∠ADC are 90°. These angles are in the semi circle. Thus, both the triangles are lying in the semi circle and AC is the diameter of the circle.
⇒ Points A, B, C and D are concyclic.
Thus, CD is the chord.
⇒ ∠CAD = ∠CBD (Angles in the same segment of the circle)

Given,
AC is the common hypotenuse. ∠B = ∠D = 90°.
To prove,
∠CAD = ∠CBD
 
Proof:
Thus, CD is the chord.
⇒ ∠CAD = ∠CBD (Angles in the same segment of the circle)