Question

Given: AC I BD and BD bisects AC.Prove: AABDACBD.StepStatementReason1AC I BDBD bisects ACGiven2AD , DCA segment bisector divides a segment into two congruent segmentstryType of StatementB

Answer 1

Ok to probe that ABD=CBD you need to prove that:

$AB\cong BC$

To prove that you have to use the Pythagorean theorem which states that given a rigth triangle abc with c as its hypotenuse:

$c^2=a^2+b^2$

In this problem AB and BC are the hypotenuses of triangles ABD and CBD respectively. So you have to use the theorem in both:

$AB=\sqrt[]{(AD)^2+(BD)^2}\text{ }$$BC=\sqrt[]{(DC)^2+(BD)^2}\cong\sqrt[]{(AD)^2+(BD)^2}=AB$

So in step 3 the type of statement would be:

$AB\cong BC$

And the reason would be: according to the pythagorean theorem

The last step would be step 4 and the statement would be:

$\Delta ABD\cong\Delta CBD$

The reason: they