Geo_Book_Answers

LESSON 13.5
1. D: Paris is in France; Tucson is in the U.S.;
London is in England. Bamako must be the capital
of Mali.
2. C: The “Sir” in part A shows that Halley was
English; Julius Caesar was an emperor, not a
scientist; Madonna is a singer. Galileo Galilei must
be the answer.
3. No, the proof is claiming only that if two
particular angles are not congruent, then the two
particular sides opposite them are not congruent. It
still might be the case that a different pair of angles
are congruent and that therefore a different pair of
sides are congruent.
4. Yes, this statement is the contrapositive of the
conjecture proved in Example B, so they are
logically equivalent.
5. 1. Assume the opposite of the conclusion;
2. Triangle Sum Theorem; 3. Substitution property
of equality; 4. 0°; Subtraction property of equality
6. Assume ZOID is equiangular. Use the definition
of equiangular and the Four Congruent Angles
Rectangle Theorem to prove that ZOID is a
rectangle. Therefore ZOID is a parallelogram, which
creates a contradiction.
7. Assume CD is the altitude to AB. Use the
definitions of altitude, median, and midpoint, the
Right Angles Are Congruent Theorem, and the
SAS Congruence Postulate to get ADC BDC.
Therefore AC BC, which creates a contradiction.
8. Assume ZO ID. Use the Opposite Sides
Parallel and Congruent Theorem to prove that
ZOID is a parallelogram, which creates a
contradiction.
9. Given: Circle O with chord AB and perpendicular
bisector CD
Show: CD passes through O
Assume CD does not pass through O. Use the Line
Postulate to construct OB and OA and the
Perpendicular Postulate to construct OE. Then use
the Isosceles Triangle Theorem, the Right Angles
Are Congruent Theorem, and the SAA Theorem to
get OEA OEB. From CPCTC and the
definition of midpoint, prove that E is the midpoint
of AB, which creates a contradiction.
C
O
10. a 75°, b 47°, c 58°
11. 42 ft3 132 ft 3
12a.
12b. 1 3
13a. A
13b. N
13c. S
13d. S
13e. A
3
3
4 12
B
D
E
A
ANSWERS TO EXERCISES 151
Answers to Exercises