Chapter 4.4, Problem 19WE

To determine

To Prove: $\overline{AL}\cong \overline{AM}$

Explanation of Solution

Given information:

In the figure shown,

  $\overline{AB}\cong \overline{AC}$

  $\overline{AL}$ and $\overline{AM}$ trisect $\angle BAC$ which means $\angle 1\cong \angle 2\cong \angle 3$ .

  

Calculation:

Using two-column proof.

Statements	Reasons
$\overline{AB}=\overline{AC}$	Given
$\angle 1\cong \angle 2\cong \angle 3$	Given
$\angle B=\angle C$	As $\overline{AB}=\overline{AC}$, $\Delta ABC$ is an isosceles triangle. Angles opposite to equal sides in an isosceles triangle are equal.
$\Delta BLA\cong \Delta CMA$	By ASA Postulate
$\overline{AL}\cong \overline{AM}$	Using congruent parts of congruent triangles

Therefore, $\overline{AL}\cong \overline{AM}$ has been proved.