Question

tw bisects ∠utv and tv ≅ tu. complete the proof that △tuw ≅ △tvw.
statement
1 tw bisects ∠utv
2 tv ≅ tu
3 ∠utw ≅ ∠vtw
4 tw ≅ tw
5
reason
given
given
definition of angle bisector
reflexive property of congruence

Explanation:

Step1: Recall the SAS (Side - Angle - Side) Congruence Criterion

Two triangles are congruent if two sides and the included angle of one triangle are congruent to two sides and the included angle of the other triangle.

Step2: Identify the sides and included angle in \(\triangle TUW\) and \(\triangle TVW\)

In \(\triangle TUW\) and \(\triangle TVW\):

• We have \(\overline{TV}\cong\overline{TU}\) (given as statement 2).
• \(\angle UTV\) is bisected by \(\overleftrightarrow{TW}\), so \(\angle UTW\cong\angle VTW\) (statement 3, definition of angle bisector).
• \(\overline{TW}\cong\overline{TW}\) (statement 4, reflexive property of congruence).

Answer:

\(\triangle TUW\cong\triangle TVW\) (by the Side - Angle - Side (SAS) Congruence Criterion)