Triangles W X Z and Y Z X share common side X Z. Angles W X Z and X Z Y are right angles. The lengths of sides W X and Z Y are 21 centimeters.

Question

Is ΔWXZ ≅ ΔYZX? Why or why not?

Yes, they are congruent by SAS.
Yes, they are both right triangles.
No, the triangles share side XZ.
No, there is only one set of congruent sides.

Answer 1

To determine if triangles ΔWXZ and ΔYZX are congruent, we can analyze the information given:

1. Both angles WXZ and XZY are right angles. This means both triangles are right triangles.
2. The lengths of sides WX and ZY are both 21 centimeters. Therefore, WX = ZY.
3. The triangles share the side XZ.

To apply the SAS (Side-Angle-Side) criterion for triangle congruence, we need two sides and the included angle to be congruent in both triangles.

• We have one pair of congruent sides: WX = ZY = 21 cm.
• The included angles that they form with the side XZ (angles WXZ and YZX) are both right angles (90°), which means they are also congruent.

Now we can conclude that we have:

• Side WX = Side ZY
• Angle WXZ = Angle YZX (both right angles)
• Side XZ is common to both triangles.

Thus, by the SAS criterion, we can say that ΔWXZ ≅ ΔYZX.

Therefore, the correct option is: Yes, they are congruent by SAS.