Question

ABC and ADC are two right triangle with the common hypotenuse AC prove that angle CAD equal to angle CBD​

Answer 1

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.

hope it helps parth ❤︎

Answer 2

Step-by-step explanation:

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.

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hope it helps parth ❤︎