Question

1. (l36) from the given statement below, select the definition, property, postulate, or theorem that leads to the statement you are asked to prove. given: \\( \overline { a b } = \overline { x y } ; \angle b \cong \angle y ; \overline { c b } \cong \overline { z y } \\) prove: \\( \delta a b c \cong \delta x y z \\) a. definition of congruent triangles b. angle-angle-side theorem c. side-angle-side postulate d. side-side-side postulate e. angle-side-angle postulate 13. (l36) from the given statement below, select the definition, property, postulate, or theorem that leads to the statement you are asked to prove. given: \\( \angle a \cong \angle x ; \overline { b c } \cong \overline { y z } ; \angle c \cong \angle z \\) prove: \\( \delta a b c \cong \delta x y z \\) a. definition of congruent triangles b. angle-angle-side theorem c. side-angle-side postulate d. side-side-side postulate e. angle-side-angle postulate

Explanation:

We are given two triangles $\triangle ABC$ and $\triangle XYZ$ with $\overline{AB}=\overline{XY}$, $\angle B\cong\angle Y$, and $\overline{CB}=\overline{ZY}$. The Side - Angle - Side (SAS) Postulate states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent. Here, $\overline{AB}$ and $\overline{CB}$ are sides of $\triangle ABC$, $\overline{XY}$ and $\overline{ZY}$ are sides of $\triangle XYZ$, and $\angle B$ (included between $\overline{AB}$ and $\overline{CB}$) is congruent to $\angle Y$ (included between $\overline{XY}$ and $\overline{ZY}$).

Answer:

C. Side - Angle - Side Postulate