Question

△stv is equilateral. complete the proof that △svw ≅ △tvu.
statement
1 △stv is equilateral
2 ∠utv ≅ ∠vsw
3 overline {sw} ≅ overline {tu}
4 overline {sv} ≅ overline {tv}
5 △svw ≅ △tvu
reason
given
given
given
definition of equilateral triangle

Explanation:

Step1: Recall the SAS (Side - Angle - Side) congruence criterion

The SAS congruence criterion states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.

Step2: Identify the sides and included angle for \(\triangle SVW\) and \(\triangle TVU\)

In \(\triangle SVW\) and \(\triangle TVU\):

• We know that \(\overline{SV}\cong\overline{TV}\) (from step 4, definition of equilateral triangle \( \triangle STV\), so \(SV = TV\)).
• \(\angle VSW\cong\angle UTV\) (given in step 2).
• \(\overline{SW}\cong\overline{TU}\) (given in step 3).

Answer:

By the SAS (Side - Angle - Side) congruence criterion.