Question

tv ≅ tu. complete the proof that △tuv ≅ △tvu.
1 tv ≅ tu given
2 tv ≅ tv reflexive property of congruence
3
4
5
6
7

Explanation:

Step1: Identify the given information

We are given that \(\overline{TV}\cong\overline{TU}\) (Statement 1).

Step2: Use the reflexive property

By the reflexive property of congruence, \(\overline{TV}\cong\overline{TV}\) (Statement 2).

Step3: Use the SSS (Side - Side - Side) congruence criterion

For \(\triangle TUV\) and \(\triangle TVU\):

• \(TU = TV\) (given)
• \(TV=TV\) (reflexive property)
• \(UV = VU\) (common side, which is also a reflexive property application for the side \(UV\) in \(\triangle TUV\) and \(VU\) in \(\triangle TVU\))

So, the statement for step 3 is \(\triangle TUV\cong\triangle TVU\) and the reason is SSS (Side - Side - Side) congruence criterion.

Answer:

Statement	Reason
2. \(\overline{TV}\cong\overline{TV}\)	Reflexive Property of Congruence
3. \(\triangle TUV\cong\triangle TVU\)	SSS (Side - Side - Side) Congruence Criterion