Question

Given:Ab congruent to CBCD bisects AbProve:triangle ADC is congruent to triangle to BDC

Answer 1

Given triangle ABC, (as shown in the diagram attached) the sides AC and CB are congruent.

Also line CD bisects line AB.

Therefore, line

`\begin{gathered} AD\cong BD \\ Angle\text{ bisector of a triangle} \\ An\text{ angle bisector of a triangle divides the opposite side into two} \\ \text{segments that are prportional }to\text{ the other two sides of the triangle} \\ \text{Hence, if CD bisects line AB, and AC}\cong BC \\ \text{Then AB}\cong BD \end{gathered}`
`\begin{gathered} \angle ACD=\angle BCD \\ \text{Angle bisector} \\ \text{If the line CD bisects line AB, and }AD\cong BD \\ \text{Then }\angle ACD\cong\angle BCD \end{gathered}`

Therefore, in both triangles, we have;

`AC\cong CB\text{ (Given)}`
`AD\cong BD\text{ (Angle bisector)}`