Chapter 6, Problem 17CR

To determine

To complete: the given statement using $<,=,\text{ or }>$ .

Answer to Problem 17CR

  $\angle 1\cong \angle 2$ and $\angle 3\cong \angle 4$ , then $AB\underset{\_}{=}AC.$

Explanation of Solution

Given information:

The given figure is as follows:

  

The given statement is “ $\angle 1\cong \angle 2$ and $\angle 3\cong \angle 4$ , then $AB\underset{\_}{}AC.$

Concept used:

Angle-side-Angle congruence theorem:

The two angles and the included side of one triangle are equal to corresponding angles and included side of another triangle, then the triangles are congruent.

In $\Delta ABT$ and $\Delta ACT$ , $\angle 1\cong \angle 2$ , $\angle 3\cong \angle 4$ and side AT is common. So, using ASA congruence theorem, the two triangles $\Delta ABT,\Delta ACT$ are congruent.

Thus, their corresponding sides are equal.

  $AB=AC.$

Hence, $AB\underset{\_}{=}AC.$