Chapter 4.6, Problem 7CYU

To determine

To prove:

  $\Delta ABE\cong \Delta CBE$ for the following figure in the form of the two-column:

  

Explanation of Solution

Given information:

  $\overline{EB}$ bisects $\angle ABC$

  $\Delta ABC$ is isosceles triangle

Proof:

From the given figure:

  

The two-column proof is written as:

No.	Steps of proof	Reason
1	$\Delta ABC$ is isosceles triangle. $\overline{EB}$ bisects $\angle ABC$	Given information
2	$\overline{AB}\cong \overline{BC}$	According to the definition of the isosceles
2	$\angle ABE\cong \angle CBE$	According to the definition of the angle bisector
3	$\overline{BE}\cong \overline{BE}$	According to the reflexive property
4	$\Delta ABE\cong \Delta CBE$	According to side angle side (SAS) congruence postulate

Hence proved