Chapter 2.2, Problem 11E

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7th Edition

Alexander + 2 others

ISBN: 9781337614085

Textbook Problem

Which of the following statements would you prove by the indirect method?

a) In triangle

b) If alternate exterior

c) If

d) If two sides of a triangle are congruent, the two angles opposite these sides are also congruent.

e) The perpendicular bisector of a line segment is unique.

To determine

(a)

Whether the statement, “In triangle

Explanation

**Approach:**

1. Suppose that

2. Reason from the supposition until you reach a contradiction.

3. Note that the supposition claiming that

Step 3 completes the proof.

**Calculation:**

Consider the given statement, “In triangle

To determine

(b)

Whether the statement, “If alternate exterior

To determine

(c)

Whether the statement, “If

To determine

(d)

Whether the statement, “If two sides of a triangle are congruent, the two angles opposite these sides are also congruent.” can be proved by the indirect method.

To determine

(e)

Whether the statement, “The perpendicular bisector of a line segment is unique” can be proved by the indirect method”.

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