Chapter 4.4, Problem 10WE

To determine

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

Answer to Problem 10WE

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

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

Explanation of Solution

Given information:

Given figure,

Given $\overline{BD}\parallel \overline{CE};\angle 5\cong \angle 6$

And,

  $\overline{BD}\parallel \overline{CE}$

  $\overline{AC}\cong \overline{AE}$

  $\angle 5\cong \angle 6;\angle 6\cong \angle 7$

  $\angle 5\cong \angle 6$

  $\angle C\cong \angle E$

Prove: $\overline{AC}\cong \overline{AE}$

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: $\overline{BD}\parallel \overline{CE};\angle 5\cong \angle 6$

Prove: $\overline{AC}\cong \overline{AE}$

Proof:

  $\angle 5\cong \angle 6$

Reason: given

  $\angle 1\cong \angle 2$

Reason: given

  $\angle 5\cong \angle 6;\angle 6\cong \angle 7$

Reason: corresponding angles

  $\angle C\cong \angle E$

Reason: Transitive property

  $\overline{AC}\cong \overline{AE}$

Reason: Converse of isosceles theorem

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:

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