   Chapter 2.2, Problem 11E Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Solutions

Chapter
Section Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085
Textbook Problem

Which of the following statements would you prove by the indirect method?a) In triangle A B C , if m ∠ A > m ∠ B , then A C ≠ B C .b) If alternate exterior ∠ 1 ≅ alternate exterior ∠ 8 , then l is not parallel to m .c) If ( x + 2 ) ⋅ ( x − 3 ) = 0 , then x = − 2   or   x = 3 .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 ABC, if mA>mB, then ACBC” can be proved by the indirect method.

Explanation

Approach:

(1) To prove the statement PQ by the indirect method, the following steps are used:

1. Suppose that Q is true.

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

3. Note that the supposition claiming that Q is true must be false and that Q must therefore be true.

Step 3 completes the proof.

(2) The sides opposite to equal angles in a triangle are also equal.

Calculation:

Consider the given statement, “In triangle ABC, if mA>mB, then ACBC

To determine

(b)

Whether the statement, “If alternate exterior 1 alternate exterior 8, then 𝓁 is not parallel to m” can be proved by the indirect method.

To determine

(c)

Whether the statement, “If (x+2)(x3)=0, then x=2orx=3” can be proved by the indirect method.

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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