Question

HELP ME WITH THE GEOMETRY PLEASE !!!! I'M REALLY IN NEED OF ​

Answer 1

Question:

If AD is the bisector of ∠A of triangle ABC, show that AB>DB and AC>DC.

As AD bisects ∠A, then ∠DAB = ∠DAC

And ∠BDA is the exterior angle of ∆DAC, so ∠BDA > ∠DAC, or ∠BDA > ∠DAB

Therefore, AB > DB as in a traingle sides opposite to a greater angle are greater in length.

In the same way, you can prove AC > DC, like so:

As AD bisects ∠A, then ∠DAB = ∠DAC

And ∠CDA is the exterior angle of ∆DAB, so ∠CDA > ∠DAB, or ∠CDA > ∠DAC

Therefore, AC > DC as in a traingle sides opposite to a greater angle are greater in length.

Hope this Helped!

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