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Which congruence theorem can be used to prove △WXZ ≅ △YZX? Triangles W X Z and Y Z X share side X Z. Angles W X Z and X Z Y are right angles. Angles X W Z and X Y Z are congruent. AAS ASA SAS HL

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Answer:

The correct option is AAS.

Step-by-step explanation:

Consider the diagram below.

  • It is provided that The triangles △ WXZ and △ YZX share a side XZ.
  • Angles ∠WXZ and ∠XZY are right angles.
  • Angles ∠XWZ and ∠XYZ are congruent.

If two angles are congruent it implies that they are same in degrees or radians.

So, the angles ∠XWZ and ∠XYZ are equal.

So, in the diagram below, one of the triangles have two angles that are equal to the corresponding angles on the other triangle and the two triangles share a side.

Then according to the Angle-Angle-Side (AAS) statement the triangles △ WXZ and △ YZX are congruent.

Thus, the correct option is AAS.

Ver imagen warylucknow

The congruence theorem that can be used to prove that △WXZ ≅ △YZX is; AAS

  • We are told that;

ΔWXZ and ΔYZX share side XZ

∠WXZ and ∠XZY are right angles

∠XWZ and ∠XYZ are congruent

  • Now, from the given parameters, we can say that from reflexive property of congruence, XZ is congruent to itself and thus, we have one side of both triangles that is congruent.

  • Secondly, since ∠WXZ and ∠XZY are right angles, it means they are equal and therefore congruent to each other.

  • Lastly, we are told that ∠XWZ and ∠XYZ are congruent.

  • In summary, we have 2 corresponding angles and one corresponding side that are equal but the corresponding side is not with the included angles and as such the triangles are congruent by AAS Congruency.

Read more about AAS Congruency at; https://brainly.com/question/7727792

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