Question

consider δwxy and δbcd with ∠x ≅ ∠c, wx ≅ bc, and wy ≅ bd. can it be concluded that δwxy ≅ δbcd by sas? why or why not?
no, because the third corresponding sides must also be given as congruent
no, because the corresponding congruent angles listed are not the included angles
no, because all corresponding angles must be given as congruent
yes, because two corresponding sides and a corresponding angle are congruent

Explanation:

Step1: Recall SAS Congruence Criterion

The SAS (Side - Angle - Side) congruence criterion 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. The included angle is the angle that is between the two given sides.

Step2: Analyze the Given Information

In $\triangle WXY$ and $\triangle BCD$, we have $\overline{WX}\cong\overline{BC}$, $\overline{WY}\cong\overline{BD}$, and $\angle X\cong\angle C$. Let's identify the sides and angles:

• In $\triangle WXY$, the sides adjacent to $\angle X$ are $\overline{WX}$ and $\overline{XY}$.
• In $\triangle BCD$, the sides adjacent to $\angle C$ are $\overline{BC}$ and $\overline{CD}$.
• We are given $\overline{WX}\cong\overline{BC}$ and $\overline{WY}\cong\overline{BD}$, but $\angle X$ is not the included angle between $\overline{WX}$ and $\overline{WY}$ (the included angle between $\overline{WX}$ and $\overline{WY}$ would be $\angle W$), and $\angle C$ is not the included angle between $\overline{BC}$ and $\overline{BD}$ (the included angle between $\overline{BC}$ and $\overline{BD}$ would be $\angle B$). So the congruent angle given is not the included angle between the two congruent sides.

Answer:

no, because the corresponding congruent angles listed are not the included angles