Chapter 4.4, Problem 9WE

To determine

To place: the statements in an appropriate order for a proof.

Answer to Problem 9WE

On the basis of proof given above appropriate order of statements is given below:

(c), (d), (b) and (a).

Explanation of Solution

Given information:

Given figure,

Given $\overline{RS}\cong \overline{RT}$

And,

  $\angle 3\cong \angle 4$

  $\angle 3\cong \angle 1;\angle 2\cong \angle 4$

  $\overline{RS}\cong \overline{RT}$

  $\angle 1\cong \angle 2$

Prove: $\angle 3\cong \angle 4$

Calculation:

The Isosceles Triangle Theorem: If two sides of a triangle are congruent, then the angles opposite to those sides are congruent.

Converse of Isosceles Theorem: If two angles of a triangle are congruent, then the sides opposite to those angles are congruent.

Given: $\overline{RS}\cong \overline{RT}$

Prove: $\angle 3\cong \angle 4$

Proof:

  $\overline{RS}\cong \overline{RT}$

Reason: given

  $\angle 1\cong \angle 2$

Reason: Isosceles Theorem.

1.   $\angle 3\cong \angle 1;\angle 2\cong \angle 4$

   Reason: Vertically opposite angles

     $\angle 3\cong \angle 4$

   Reason: Transitive property

   In this arrange statements given in the problem in appropriate order for a proof.

   Answers may vary for this.

   On the basis of proof given above appropriate order of statements is given below:

   (c), (d), (b) and (a).