Chapter 4.4, Problem 23PPS

(a)

To determine

To prove:

  $\Delta ACB\cong \Delta ACD$

Explanation of Solution

Given information:

  

  $\overline{TS}\cong \overline{SF}\cong \overline{FR}\cong \overline{RT}$

  $\angle TSF,\angle SFR,\angle FRTand\angle RTS$ are right angles.

Proof:

Proof	Reason
$\overline{TS}\cong \overline{SF}\cong \overline{FR}\cong \overline{RT}$	Given.
$\angle TSF,\angle SFR,\angle FRTand\angle RTS$ are right angles.	Given.
$\angle STR\cong \angle TRF$	All right angles are congruent.
$\Delta STR\cong \Delta TRF$	SAS − Side, Angle, Side.
$\overline{RS}\cong \overline{TF}$	CPCTC.

(b)

To determine

To prove:

  $\angle SRT\cong \angle SRF$

Explanation of Solution

Given information:

  

  $\overline{TS}\cong \overline{SF}\cong \overline{FR}\cong \overline{RT}$

  $\angle TSF,\angle SFR,\angle FRTand\angle RTS$ are right angles.

Proof:

Proof	Reason
$\overline{TS}\cong \overline{SF}\cong \overline{FR}\cong \overline{RT}$	Given.
$\angle TSF,\angle SFR,\angle FRTand\angle RTS$ are right angles.	Given.
$\angle STR\cong \angle SFR$	All right angles are congruent.
$\Delta STR\cong \Delta SFR$	SAS − Side, Angle, Side.
$\angle SRT\cong \angle SRF$	CPCTC.