Question

△stv is equilateral. complete the proof that △svw ≅ △tvu.

1 △stv is equilateral
2 overline {sw} ≅ overline {tu}
3 ∠utv ≅ ∠vsw
4 overline {sv} ≅ overline {tv}
5 △svw ≅ △tvu

Explanation:

Step1: Given

$\triangle STV$ is equilateral (given in the problem statement).

Step2: Given

$\overline{SW}\cong\overline{TU}$ (given in the problem's proof - setup, likely from the figure's markings).

Step3: Given

$\angle UTV\cong\angle VSW$ (given in the problem's proof - setup, likely from the figure's markings).

Step4: Property of equilateral triangle

Since $\triangle STV$ is equilateral, all its sides are equal. So, $\overline{SV}\cong\overline{TV}$ (by the definition of an equilateral triangle: all sides of an equilateral triangle are congruent).

Step5: SAS (Side - Angle - Side) congruence criterion

We have two sides ($\overline{SW}\cong\overline{TU}$ and $\overline{SV}\cong\overline{TV}$) and the included angle ($\angle UTV\cong\angle VSW$) congruent. By the SAS (Side - Angle - Side) congruence criterion, $\triangle SVW\cong\triangle TVU$.

Answer:

1. Reason: Given
2. Reason: Given
3. Reason: Given
4. Reason: Definition of equilateral triangle
5. Reason: SAS (Side - Angle - Side)