Question

w is the midpoint of su and ∠u ≅ ∠s. complete the proof that △svw ≅ △utw.
statement
1 w is the midpoint of su
2 ∠u ≅ ∠s
3 sw ≅ uw
4 ∠swv ≅ ∠twu
5 △svw ≅ △utw
reason
given
given
vertical angle theorem

Explanation:

Step1: Midpoint definition

By the definition of a midpoint, if \(W\) is the midpoint of \(\overline{SU}\), then \(SW = UW\), so \(\overline{SW}\cong\overline{UW}\)

Step2: ASA congruence criterion

We have \(\angle U\cong\angle S\) (given), \(\overline{SW}\cong\overline{UW}\) (from step 1), and \(\angle SWV\cong\angle TWU\) (Vertical Angle Theorem). By the Angle - Side - Angle (ASA) congruence criterion, \(\triangle SVW\cong\triangle UTW\)

Answer:

1. Definition of midpoint; 5. ASA (Angle - Side - Angle)