Preparing for the Regents Examination Geometry, AK

6 True
7 True
8 True
9 True
10 Answers will vary. One possible answer is:
Every square has four sides or every triangle
has three sides. True
11 Answers will vary. One possible answer is:
The sum of the measures of the angles of
every triangle is 180 and every triangle has
four angles. False
2-3 Conditionals
(pages 26–27)
1 (2) You take this medicine.
2 (1) I will stay in this afternoon.
3 (1) true
4 (1) true
5 (1) true
6 Conditional
7 Conjunction
8 Conditional
9 Disjunction
10 Negation
11 Answers will vary. x 18 is one possible
answer.
12 x 2
13 Any positive number or zero
14 Any perfect square that is not even
15 Answers will vary. x √ 2 is one possible
answer.
16 True
17 False
18 The sun is
shining.
It is not
raining.
If the sun is
shining, it is
not raining.
Sunny T T T
Sun
showers
T F F
Cloudy F T T
Stormy F F T
4 Chapter 2: Logic
2-4 Converses, Inverses,
and Contrapositives
(pages 28–29)
1 (1) If you stop your car, then the traffic light
is red.
2 (3) If the sum of two numbers is not even,
then the numbers are not both even.
3 (1) If the merrygoround was not oiled, then
it will squeak.
4 (2) If we are on vacation, it is summer.
5 (4) If a triangle is not equilateral, then it
does not have three congruent angles.
6 (2) If I didn’t turn on the air conditioner,
then the house isn’t cool.
7 (2) disjunction, p ∨ q
8 Converse: If school is open, then it is September.
Inverse: If it is not September, then school is
not open.
Contrapositive: If school is not open, then it is
not September.
9 Converse: If the figure has four sides, then it
is a square.
Inverse: If the figure is not a square, then it
does not have four sides.
Contrapositive: If the figure does not have
four sides, then it is not a square.
10 Converse: If someone will trade desserts, then
I have cookies with my lunch.
Inverse: If I do not have cookies with my
lunch, then someone will not trade desserts.
Contrapositive: If someone will not trade
desserts, then I do not have cookies with
my lunch.
11 Converse: If my teacher will be able to read
my paper, then I typed it.
Inverse: If I do not type my paper, then my
teacher will not be able to read it.
Contrapositive: If my teacher will not be able
to read my paper, then I did not type it.
12 Converse: If I am late to school, then I didn’t
set my alarm.
Inverse: If I set my alarm, then I will not be
late to school.
Contrapositive: If I am not late to school, then
I set my alarm.