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? no, there is not enough information given. no, the sides of the triangles intersect. yes, along with the given information, \\( \overline{zx} \cong \overline{zx} \\) by the reflexive property. yes, the triangles are both obtuse.

Explanation:

Step1: Recall the SAS (Side - Angle - Side) congruence criterion

For two triangles \(\triangle VZX\) and \(\triangle WXZ\), the SAS 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: Analyze the given information

We are given \(VX = WZ=40\mathrm{cm}\) and \(m\angle ZVX=m\angle XWZ = 22^{\circ}\). Also, by the reflexive property of congruence, \(ZX\cong ZX\). In \(\triangle VZX\) and \(\triangle WXZ\), we have \(VX = WZ\), \(\angle ZVX=\angle XWZ\) and \(ZX = ZX\). The angle is included between the two sides (for \(\triangle VZX\), the sides are \(VX\) and \(ZX\) with included angle \(\angle ZVX\); for \(\triangle WXZ\), the sides are \(WZ\) and \(ZX\) with included angle \(\angle XWZ\)).

Answer:

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