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Five-Minute Check (over Lesson 105) NGSSS Then/No
w New Vocabulary Theorem 10.12 Example 1 Use
Intersecting Chords or Secants Theorem
10.13 Example 2 Use Intersecting Secants and
Tangents Theorem 10.14 Example 3 Use Tangents
and Secants that Intersect Outside a
Circle Example 4 Real-World Example Apply
Properties of Intersecting Secants Concept
Summary Circle and Angle Relationships
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5-Minute Check 1
A. yes B. no

• A
• B

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5-Minute Check 2
A. yes B. no

• A
• B

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5-Minute Check 3
Find x. Assume that segments that appear to be
tangent are tangent.
A. 10 B. 11 C. 12 D. 13

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

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5-Minute Check 4
Find x. Assume that segments that appear to be
tangent are tangent.

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

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5-Minute Check 5

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

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NGSSS
MA.912.G.6.2 Define and identify circumference,
radius, diameter, arc, arc length, chord, secant,
tangent and concentric circles. MA.912.G.6.4
Determine and use measures of arcs and related
angles. Also addresses MA.912.G.6.3.
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Then/Now
You found measures of segments formed by tangents
to a circle. (Lesson 105)

• Find measures of angles formed by lines
  intersecting on or inside a circle.

• Find measures of angles formed by lines
  intersecting outside the circle.

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Vocabulary

• secant

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Concept
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Example 1
Use Intersecting Chords or Secants
A. Find x.
Theorem 10.12
Substitution
Simplify.
Answer x 82
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Example 1
Use Intersecting Chords or Secants
B. Find x.
Step 1 Find m?VZW.
Theorem 10.12
Substitution
Simplify.
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Example 1
Use Intersecting Chords or Secants
Step 2 Find m?WZX.
?WZX 180 ?VZW Definition of
supplementary angles x 180
79 Substitution x 101 Simplify. Answer x
101
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Example 1
Use Intersecting Chords or Secants
C. Find x.
Theorem 10.12
Substitution
Multiply each side by 2.
Subtract 25 from each side.
Answer x 95
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Example 1
A. Find x.
A. 92 B. 95 C. 98 D. 104

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

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Example 1
B. Find x.
A. 92 B. 95 C. 97 D. 102

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

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Example 1
C. Find x.
A. 96 B. 99 C. 101 D. 104

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

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Concept
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Example 2
Use Intersecting Secants and Tangents
A. Find m?QPS.
Theorem 10.13
Substitute and simplify.
Answer m?QPS 125
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Example 2
Use Intersecting Secants and Tangents
Theorem 10.13
Substitution
Multiply each side by 2.
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Example 2
A. Find m?FGI.
A. 98 B. 108 C. 112.5 D. 118.5

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

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Example 2
A. 99 B. 148.5 C. 162 D. 198

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

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Concept
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Example 3
Use Tangents and Secants that Intersect Outside a
Circle
Theorem 10.14
Substitution
Multiply each side by 2.
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Example 3
Use Tangents and Secants that Intersect Outside a
Circle
Subtract 141 from each side.
Multiply each side by 1.
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Example 3
Use Tangents and Secants that Intersect Outside a
Circle
Theorem 10.14
Substitution
Multiply each side by 2.
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Example 3
Use Tangents and Secants that Intersect Outside a
Circle
Add 140 to each side.
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Example 3
A. 23 B. 26 C. 29 D. 32

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

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Example 3
A. 194 B. 202 C. 210 D. 230

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

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Example 4
Apply Properties of Intersecting Secants
Theorem 10.14
Substitution
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Example 4
Apply Properties of Intersecting Secants
Multiply each side by 2.
Subtract 96 from each side.
Multiply each side by 1.
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Example 4

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

A. 25 B. 35 C. 40 D. 45
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Concept
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End of the Lesson