Chapter 4, Problem 3CT

To determine

To complete: the proof.

Answer to Problem 3CT

  $\overline{AB}\cong \overline{XY}$ and $\overline{AC}\cong \overline{XZ}$ by SAS postulate must show that $\angle A\cong \angle X$ and to prove that $\Delta ABC\cong \Delta XYZ$ by SSS postulate must show that $\overline{BC}\cong \overline{YZ}$ .

Explanation of Solution

Given information:

Prove $\Delta ABC\cong \Delta XYZ$ . Shown $\overline{AB}\cong \overline{XY}$ and $\overline{AC}\cong \overline{XZ}$ . To prove the triangles congruent by SAS must show that $-\cong -$ . To prove the triangles congruent by SSS must show that $-\cong -$ .

Calculation:

SSS Postulate: If three sides of a triangle are equal to the three corresponding sides of another triangle, then the triangles are congruent.

SAS Postulate: If two sides and the angle included between them of a triangle are equal to the two corresponding sides and the angle included between them of another triangle, then the triangles are congruent.

  

Given: $\overline{AB}\cong \overline{XY}$ and $\overline{AC}\cong \overline{XZ}$ by SAS postulate must show that $\angle A\cong \angle X$ and to prove that $\Delta ABC\cong \Delta XYZ$ by SSS postulate must show that $\overline{BC}\cong \overline{YZ}$ .