Question

write each proof. for the following proofs #1 - 2, fill in the missing statement or reason by using the statements in the statement bank. you may use each statement once, not at all, or more than once. statement bank: def. of angle bisector, $overline{ad}congoverline{cd}$, def. of segment bisector, $overline{cd}congoverline{gh}$, given, $angle tsvcongangle tsw$, transitive property of congruence, quadrilateral $abcdcong$ quadrilateral $efgh$. 1. given: $\triangle svtcong\triangle swt$. prove: $overline{st}$ bisects $angle vsw$. statements reasons 1. $\triangle svtcong\triangle swt$ 1. 2. 2. corresponding parts of congruent figures are congruent. 3. $overline{st}$ bisects $angle vsw$. 3. 2. given: quadrilateral $abcdcong$ quadrilateral $efgh$, $overline{ad}congoverline{cd}$. prove: $overline{ad}congoverline{gh}$. statements reasons 1. 1. given 2. 2. given 3. 3. corresponding parts of congruent figures are congruent. 4. $overline{ad}congoverline{gh}$ 4.

Explanation:

Step1: State given information

1. $\triangle SVT\cong\triangle SWT$ (Given)

Step2: Identify congruent angles

1. $\angle VST\cong\angle WST$ (Corresponding parts of congruent figures are congruent)

Step3: Apply angle - bisector definition

1. $\overline{ST}$ bisects $\angle VSW$ (Definition of angle bisector)

for second proof:

Step1: State first given

1. Quadrilateral $ABCD\cong$ Quadrilateral $EFGH$ (Given)

Step2: State second given

1. $\overline{AD}\cong\overline{CD}$ (Given)

Step3: Use congruent - figure property

1. $\overline{AD}\cong\overline{GH}$ (Corresponding parts of congruent figures are congruent)

Answer:

Statements	Reasons
2. $\angle VST\cong\angle WST$	2. Corresponding parts of congruent figures are congruent
3. $\overline{ST}$ bisects $\angle VSW$	3. Definition of angle bisector