Question

1. heres a diagram. $overline{xy} cong overline{zw}$, $overline{xz} cong overline{wy}$, and $angle wxz cong angle yzx$. which congruence statements are true?

a. triangles xyz and ywz are congruent by asa
b. triangles xyz and zwy are congruent by sss
c. triangles xyz and zwy are congruent by sas
d. triangles xyz and wzy are congruent by sas
e. triangles xyz and wzy are congruent by ssa
e. not enough information

Explanation:

Step1: Analyze the given congruent parts

We are given that \(\overline{XY}\cong\overline{ZW}\), \(\overline{XZ}\cong\overline{WY}\), and \(\angle WXZ\cong\angle YZX\).

Step2: Check the congruence criteria

For triangles \(XYZ\) and \(ZWY\):

• We have two pairs of sides \(\overline{XY}\cong\overline{ZW}\), \(\overline{XZ}\cong\overline{WY}\)
• The included angle: \(\angle XYZ\) (for \(\triangle XYZ\)) and \(\angle ZWY\) (for \(\triangle ZWY\)) are equal because of the given side - side - side relationships and the properties of the figure.

By the SAS (Side - Angle - Side) congruence criterion, 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.

Answer:

C. Triangles \(XYZ\) and \(ZWY\) are congruent by \(SAS\)