Identify the missing parts in the proof. given: ∠abc is a right angle. db bisects ∠abc. prove: m∠cbd = 45°

Answer with Step-by-step explanation:

We are given that

Angle ABC is  a right angle .

DB bisects the angle ABC.

We have to prove that

When DB bisects the angle ABC

Substitute the value

Hence, proved.

When an angle is bisected, then it would be divided into two equal parts. Thus, bisection of <B implies m∠CBD = 45°.

Bisection of angle implies that the angle would be divided into two equal parts.

Given that ΔABC is a right angled triangle.  Thus since <ABC is right angle, it implies that the measure of the angle is .

Then;

DB is not perpendicular to AC

m<A + m<ABD + m<ADB = (sum of angles in a triangle)

Also,

m<C + m<CBD + m<CDB = (sum of angles in a triangle)

Since DB is a bisector of right angle B, then;

m<B = m<ABD + m<CBD (bisection property of an angle)

= m<ABD + m<CBD

But,

m<ABD ≅ m<CBD (similarity property)

So that:

= 2<CBD

m<CBD =

          =

m<CBD =

Thus, the measure of angle CBD = ABD =

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