Download Answers to Lesson 2-1 through 2

Answers to Lesson 2-1 through 2-6 extra practice
Lesson 2-1
1. False. You could use the drawing below, which shows an example in which A, B, C,
and D would not be collinear. Remember that if you can come up with one
counterexample to the conjecture, you have proven that the conjecture is false.
A
B
C
2.
3.
4.
5.
6.
D
True. Any real number squared will always be nonnegative
False. If you plot these points, you will see that they do not make up a square
Conjecture: Angles ABC and angles DBE are congruent angles.
Conjecture: Lines l and m are perpendicular to each other.
Conjecture: Angles QRS and QRT are supplementary angles.
Lesson 2-2
1. Hypothesis: A container holds 32 ounces; conclusion: it holds a quart
2. Hypothesis: A candy bar is a Milky Way ®; conclusion: it contains caramel
3. If the angles are right angles, then they are congruent
4. If it is a car, then it has four wheels
5. If it is a triangle, then it contains exactly 3 angles
6. Answers follow below
a. Converse: If the distance of a race is about 6.2 miles, then it is 10
kilometers-true
b. Inverse: If the distance of a race is not 10 kilometers, then it is not about
6.2 miles-true
c. Contrapositive: If the distance of a race is not about 6.2 miles, then it is
not 10 kilometers-true
7. Answers follow below
a. Converse: If it is a fruit, then it is an apple-false
b. Inverse: If it is not an apple, then it is not a fruit-false
c. Contrapositive: If it is not a fruit, then it is not an apple-true
Lesson 2-3
1. Invalid-an easy way to think of this is that you cannot conclude that just because
Kris has to pass a physical examination, that he must be a pilot. Plenty of people
(like teachers!) have to take physical examinations.
2. Statement (3) follows (1) and (2) from the Law of Detachment
3. Yes, a conclusion can be reached: Basalt was formed by volcanoes-Law of
Syllogism
4. No conclusion. For there to have been a valid conclusion possible, statement (2)
would have had to read something like “A quadrilateral is a rectangle”, which
would have led to a conclusion like “A quadrilaterial has four right angles” (Law
of Detachment). Statement (2) also could have read something like “If something
has four right angles, the sum of the angles is 360, which would have led to a
conclusion like “If a quadrilateral is a rectangle, then the sum of its angles is 360”
(Law of Syllogism). This one’s a little complicated, so don’t expect anything this
difficult on the test.
Lesson 2-4 (study chapter 2 postulates and theorems on p. 806-807)
1. Substitution (=)
2. Addition (=) because you’re adding first 2 equations
3. The reasons follow below
1. Given
2. Multiplication (=)
3. Distribution (=)
4. Addition (=)
5. Division (=)
6. Symmetric (=)
Lesson 2-5
1. Division (=)
2. Addition (=)
3. Substitution (=)
4. This one’s a little complicated, so don’t expect anything this difficult on the test.
5. This one’s a little complicated, so don’t expect anything this difficult on the test.
Lesson 2-6
1. sometimes
2. always
3. never
4. Answers follow below
a. Angles 2 and 5
b. Angles 1 and 4
c. Angles 6 and 3
5. Answers follow below
a. Angles UWQ and QWR
b. Angles VWQ and QWS
c. Angles QWR and RWT
d. Angles QWS and SWT
e. Angles RWS and SWU
f. Angles SWT and TWV
g. Angles RWT and TWU
h. Angles VWU and SWU
6. Angles 1 and 4 are vertical angles, so they are congruent. To solve for x, then, we
set m<1 = m<4, as follows
4x + 14 = 3x + 33
after subtracting 3x from both sides we have
x + 14 = 33
and after subtracting 14 from both sides we have
x = 19
since we now know that x = 19, we can substitute 19 in for x in m<4, giving us
3x + 33 = 3(19) + 33 = 57 + 33 = 90
7. Since <2 and <3 are complementary, we know that the sum of these two angles is
90. So we can do the following
m<2 + m<3 = 90
after substituting,
2x – 14 + x + 17 = 90
and after combining like terms
3x + 3 = 90
and after subtracting 3 from both sides, we have
3x = 87
and after dividing both sides by 3, we have
x = 29
since we now know that x = 29, we can substitute 29 in for x in m<3, giving us
m<3 = x +17 = 29 + 17 = 46
8. <5 and <UWQ are supplementary angles, which means that they add up to 180.
So we can add <5 and <UWQ together and set them equal to 180 as follows
m<5 + m<UWQ = 180
after substituting we have
3x – 7 + 8x = 180
after combining like terms, we have
11x – 7 = 180
and after adding 7 to both sides we have
11x = 187
and after dividing both sides by 11, we have
x = 17
since we now know that x = 17, we can substitute 17 in for x in m<UWQ, giving us
m<UWQ = 8x = 8*17 = 136