What additional piece of information is needed to prove the two triangles congruent using SAS?

Question

(1 point)
Responses

∠UWK ≅ ∠KMV
∠UWK ≅ ∠KMV

MK¯¯¯¯¯¯¯¯¯¯ ≅ WU¯¯¯¯¯¯¯¯¯
MK¯¯¯¯¯¯¯¯¯¯ ≅ WU¯¯¯¯¯¯¯¯¯

VM¯¯¯¯¯¯¯¯¯ ≅ WV¯¯¯¯¯¯¯¯¯
VM¯¯¯¯¯¯¯¯¯ ≅ WV¯¯¯¯¯¯¯¯¯

∠VKM ≅ ∠VUW
∠VKM ≅ ∠VUW
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Answer 1

To prove two triangles congruent using the Side-Angle-Side (SAS) congruence criterion, you need two sides of one triangle to be congruent to two sides of the other triangle, and the included angle between those two sides to be congruent.

In the information provided, you have:

1. Angles ∠UWK ≅ ∠KMV
2. Sides MK ≅ WU
3. Side VM and WV, which may or may not be the necessary sides for SAS.

Thus, you need one of the following pieces of information to satisfy the SAS criterion:

• The included angle between the two pairs of congruent sides (for instance, an angle like ∠VKM ≅ ∠VUW would be required if VM and WV were the sides).

Based on the provided options:

• The additional piece of information needed would be ∠VKM ≅ ∠VUW so that you can have two pairs of congruent sides with the included angle confirmed, allowing you to use the SAS congruence criterion effectively.