Me! provide statements and reasons for the proof of the triangle angle bisector theorem. given: line bd bisects ∠abc. auxiliary line ea is drawn such that line ae line bd | |. auxiliary line be is an extension of line bc. prove: ad/dc = ab/bc

Refer to the attached image.

Given: Line BD bisects ∠ABC.

Construction: Auxiliary Line EA is drawn such that Line AE is parallel to Line BD . Auxiliary Line BE is an extension of Line BC.

To prove:

Proof:

Since Lines EA and BD are parallel,

(Corresponding angles)

So, (Alternate angles)

(because it is given that BD bisects ∠ABC )

So, by the above three equations, we get

So, BE=AB (Opposite sides equal to opposite angles are equal) (Equation 1)

Now, consider triangle ACE,

Since AE is parallel to BD.

By Basic Proportionality theorem, which states

" If a line is drawn parallel to one side of a triangle intersecting other two sides, then it divides the two sides in the same ratio."

So,we get

By using equation 1, we get

Hence, proved.

2/5

step-by-step explanation: