   Chapter 2.2, Problem 12E 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) If A C > A B in Δ A B C , then m ∠ B ≠ m ∠ C .b) If A C = A B in Δ A B C , then m ∠ B = m ∠ C .c) If RSTV is not a square, then R S ≠ S T .d) An angle has exactly one bisector.

To determine

(a)

Whether the statement, “If AC>AB in ΔABC, then mBmC” 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, “If AC>AB in ΔABC, then mBmC

To determine

(b)

Whether the statement, “If AC=AB in ΔABC, then mB=mC” can be proved by the indirect method.

To determine

(c)

Whether the statement, “If RSTV is not a square, then RSST” can be proved by the indirect method.

To determine

(d)

Whether the statement, “An angle has exactly one bisector” can be proved by the indirect method.

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