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

Question

ABC and ADC are two right triangles with common hypotenuse AC. Prove that &#x2220; CAD = &#x2220; CBD

Philoid · Accepted Answer

It is given in the question that,

Ac is the common hypotenuse

So, B = D = 90^o

We have to prove that,

∠CAD = ∠CBD

Proof: We know that,

∠ABC and ∠ADC are 90^o as these angles are in the semi-circle

Thus, both the triangles are lying in the semi-circle and both have same diameter i.e. AC

Points A, B, C and D are concyclic

Therefore, CD is the chord

So,

∠CAD = ∠CBD (As, angles in the same segment are equal)