Question

6
given: (overline{ty}congoverline{xy},angle tvycongangle xwy)
prove: (\triangle tvycong\triangle xwy)

Explanation:

Step1: Write the given information

• Statements: $\overline{TY}\cong\overline{XY}$, $\angle TVY\cong\angle XWY$
• Reasons: Given

Step2: Identify the vertical angles

• Statements: $\angle T Y V\cong\angle X Y W$
• Reasons: Vertical angles are congruent

Step3: Apply the ASA (Angle - Side - Angle) congruence criterion

• Statements: $\triangle TVY\cong\triangle XWY$
• Reasons: ASA ( $\angle TVY\cong\angle XWY$, $\overline{TY}\cong\overline{XY}$, $\angle T Y V\cong\angle X Y W$ )

Answer:

Statements	Reasons
2. $\angle T Y V\cong\angle X Y W$	Vertical angles are congruent
3. $\triangle TVY\cong\triangle XWY$	ASA