Question

if vx = wz = 40 cm and m∠zvx = m∠xwz = 22°. can △vzx and △wxz 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

SAS (Side - Angle - Side) requires two sides and the included angle of one triangle to be congruent to two sides and the included angle of another triangle.

Step2: Analyze given information

We are given that $VX = WZ=40$ cm and $\angle ZVX=\angle XWZ = 22^{\circ}$. Also, $ZX$ is common to both $\triangle VZX$ and $\triangle WXZ$ (by the reflexive property of congruence, $\overline{ZX}\cong\overline{ZX}$). So we have two sides ($VX\cong WZ$ and $ZX\cong ZX$) and the included angles ($\angle ZVX\cong\angle XWZ$) congruent.

Answer:

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