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