Question

if vx = wz = 40 cm and m∠zvx = m∠xwz = 22°, can δvzx and δwxz be proven congruent by sas? why or why not? yes, along with the given information, zx ≅ zx by the reflexive property. yes, the triangles are both obtuse. no, the sides of the triangles intersect. no, there is not enough information given.

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.

Step2: Identify given information

We are given that $VX = WZ=40$ cm and $\angle ZVX=\angle XWZ = 22^{\circ}$. Also, $\overline{ZX}=\overline{ZX}$ by the reflexive property. In $\triangle VZX$ and $\triangle WXZ$, $VX$ and $WZ$ are the sides, $\angle ZVX$ and $\angle XWZ$ are the included angles, and $\overline{ZX}$ is common to both triangles.

Answer:

A. Yes, along with the given information, $\overline{ZX}\cong\overline{ZX}$ by the reflexive property.