Question
What additional piece of information is needed to prove the two triangles congruent using SAS?
(1 point)
Responses
VM¯¯¯¯¯¯¯¯¯ ≅ WV¯¯¯¯¯¯¯¯¯
VM¯¯¯¯¯¯¯¯¯ ≅ WV¯¯¯¯¯¯¯¯¯
∠VKM ≅ ∠VUW
∠VKM ≅ ∠VUW
∠UWK ≅ ∠KMV
∠UWK ≅ ∠KMV
MK¯¯¯¯¯¯¯¯¯¯ ≅ WU¯¯¯¯¯¯¯¯¯
Answers
GPT-4o mini
To prove the two triangles congruent using the SAS (Side-Angle-Side) postulate, we need one pair of sides and the included angle to be congruent between the two triangles.
In this case, you already have the sides VM ≅ WV, and you also have the angle ∠VKM ≅ ∠VUW, which is included between the sides.
To satisfy the SAS condition:
- We already have the congruence of the sides (VM and WV).
- We also have the angle (∠VKM and ∠VUW).
Now, we need one additional piece of information that provides the congruence of one more pair of corresponding sides.
From the available options, the **MK ≅ WU** segment provides the necessary additional information.
So, the additional piece of information needed to prove the two triangles congruent using SAS is:
**MK¯¯¯¯¯¯¯¯¯¯ ≅ WU¯¯¯¯¯¯¯¯¯**.
In this case, you already have the sides VM ≅ WV, and you also have the angle ∠VKM ≅ ∠VUW, which is included between the sides.
To satisfy the SAS condition:
- We already have the congruence of the sides (VM and WV).
- We also have the angle (∠VKM and ∠VUW).
Now, we need one additional piece of information that provides the congruence of one more pair of corresponding sides.
From the available options, the **MK ≅ WU** segment provides the necessary additional information.
So, the additional piece of information needed to prove the two triangles congruent using SAS is:
**MK¯¯¯¯¯¯¯¯¯¯ ≅ WU¯¯¯¯¯¯¯¯¯**.