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Five-Minute Check (over Lesson 2–5)
CCSS
Then/Now
New Vocabulary
Key Concept: Properties of Real Numbers
Example 1: Justify Each Step When Solving an Equation
Example 2: Real-World Example: Write an Algebraic Proof
Example 3: Write a Geometric Proof
Over Lesson 2–5
In the figure shown, A, C, and
lie in plane R, and B is on
.
Which option states the postulate
that can be used to show that A, B,
and C are collinear?
A. A line contains at
least two points.
B. A line contains only
two points.
C. A line contains at
least three points.
D. A line contains only
three points.
Over Lesson 2–5
In the figure shown, A, C, and
lie in plane R, and B is on
.
Which option states the postulate
that can be used to show that
lies in plane R?
A. Through two points, there is exactly
one line in a plane.
B. Any plane contains an infinite
number of lines.
C. Through any two points on the same
line, there is exactly one plane.
D. If two points lie in a plane, then the
entire line containing those points
lies in that plane.
Over Lesson 2–5
In the figure shown, A, C, and
lie in
plane R, and B is on
. Which option
states the postulate that can be used
to show that A, H, and D are coplanar?
A. Through any two points on the same
line, there is exactly one plane.
B. Through any three points not on the
same line, there is exactly one plane.
C. If two points lie in a plane, then the
entire line containing those points
lies in that plane.
D. If two lines intersect, then their
intersection lies in exactly one plane.
Over Lesson 2–5
In the figure shown, A, C, and
lie in plane R, and B is on
.
Which option states the postulate
that can be used to show that E
and F are collinear?
A. Through any two points, there is
exactly one line.
B. A line contains only two points.
C. If two points lie in a plane, then
the entire line containing those
points lies in that plane.
D. Through any two points, there
are many lines.
Over Lesson 2–5
In the figure shown, A, C, and
lie in plane R, and B is on
.
Which option states the postulate
that can be used to show that
intersects
at point B?
A.
The intersection point of two lines lies
on a third line, not in the same plane.
B.
If two lines intersect, then their
intersection point lies in the same plane.
C.
The intersection of two lines does
not lie in the same plane.
D.
If two lines intersect, then their
intersection is exactly one point.
Over Lesson 2–5
Which of the following numbers is an example of
an irrational number?
A. –7
B.
C.
D. 34
Content Standards
Preparation for G.CO.9 Prove theorems
about lines and angles.
Mathematical Practices
3 Construct viable arguments and critique
the reasoning of others.
You used postulates about points, lines, and
planes to write paragraph proofs.
• Use algebra to write two-column proofs.
• Use properties of equality to write geometric
proofs.
• algebraic proof
• two-column proof
• formal proof
Justify Each Step When Solving an Equation
Solve 2(5 – 3a) – 4(a + 7) = 92.
Algebraic Steps
2(5 – 3a) – 4(a + 7) = 92
Properties
Original equation
10 – 6a – 4a – 28 = 92
Distributive Property
–18 – 10a = 92
Substitution Property
–18 – 10a + 18 = 92 + 18
Addition Property
Justify Each Step When Solving an Equation
–10a = 110
Substitution Property
Division Property
a = –11
Answer: a = –11
Substitution Property
Solve –3(a + 3) + 5(3 – a) = –50.
A. a = 12
B. a = –37
C. a = –7
D. a = 7
Write an Algebraic Proof
Begin by stating what is given and what you are to prove.
Write an Algebraic Proof
Proof:
Statements
Reasons
1. d = 20t + 5
1. Given
2. d – 5 = 20t
2. Addition Property of Equality
3.
4.
=t
3. Division Property of Equality
4. Symmetric Property of
Equality
Which of the following statements would complete
the proof of this conjecture?
If the formula for the area of a trapezoid is
, then the height h of the trapezoid is
given by
.
Proof:
Statements
Reasons
1.
1. Given
?
2. _____________
2. Multiplication Property of
Equality
3.
3. Division Property of Equality
4.
4. Symmetric Property of
Equality
A. 2A = (b1 + b2)h
B.
C.
D.
Write a Geometric Proof
If A B, mB = 2mC, and mC = 45, then
mA = 90. Write a two-column proof to verify this
conjecture.
Write a Geometric Proof
Proof:
Statements
Reasons
1. A B;
mB = 2mC;
mC = 45
1. Given
2. mA = mB
2. Definition of
3. mA = 2mC
3. Transitive Property of
Equality
4. mA = 2(45)
4. Substitution
5. mA = 90
5. Substitution
angles
Proof:
Statements
1.
2.
Reasons
1. Given
?
2. _______________
3. AB = RS
3. Definition of congruent
segments
4. AB = 12
4. Given
5. RS = 12
5. Substitution
A. Reflexive Property of Equality
B. Symmetric Property of Equality
C. Transitive Property of Equality
D. Substitution Property of Equality