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Lesson Menu
Five-Minute Check (over Lesson 25) NGSSS 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
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5-Minute Check 1
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.

1. A
2. B
3. C
4. D

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5-Minute Check 2
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.

1. A
2. B
3. C
4. D

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5-Minute Check 3
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.

1. A
2. B
3. C
4. D

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5-Minute Check 4
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.

1. A
2. B
3. C
4. D

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5-Minute Check 5

1. A
2. B
3. C
4. D

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.
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5-Minute Check 6
Which of the following numbers is an example of
an irrational number?

1. A
2. B
3. C
4. D

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NGSSS
MA.912.G.8.4 Make conjectures with justifications
about geometric ideas. Distinguish between
information that supports a conjecture and the
proof of a conjecture. MA.912.G.8.5 Write
geometric proofs, including proofs by
contradiction and proofs involving coordinate
geometry. Use and compare a variety of ways to
present deductive proofs, such as flow charts,
paragraphs, two-column, and indirect proofs.
Also addresses MA.912.D.6.4.
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Then/Now
You used postulates about points, lines, and
planes to write paragraph proofs. (Lesson 25)

• Use algebra to write two-column proofs.

• Use properties of equality to write geometric
  proofs.

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Vocabulary

• algebraic proof

• two-column proof
• formal proof

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Concept
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Example 1
Justify Each Step When Solving an Equation
Solve 2(5 3a) 4(a 7) 92.
Algebraic Steps Properties 2(5 3a) 4(a
7) 92 Original equation 10 6a 4a
28 92 Distributive Property 18
10a 92 Substitution Property 18 10a 18
92 18 Addition Property
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Example 1
Justify Each Step When Solving an Equation
10a 110 Substitution Property
Division Property
a 11 Substitution Property
Answer a 11
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Example 1
Solve 3(a 3) 5(3 a) 50.
A. a 12 B. a 37 C. a 7 D. a 7

1. A
2. B
3. C
4. D

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Example 2
Write an Algebraic Proof
Begin by stating what is given and what you are
to prove.
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Example 2
Write an Algebraic Proof
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Example 2
Which of the following statements would complete
the proof of this conjecture?
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Example 2
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Example 2

1. A
2. B
3. C
4. D

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Example 3
Write a Geometric Proof
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Example 3
Write a Geometric Proof
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Example 3
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Example 3
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Example 3
A. Reflexive Property of Equality B. Symmetric
Property of Equality C. Transitive Property of
Equality D. Substitution Property of Equality

1. A
2. B
3. C
4. D

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End of the Lesson