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Five-Minute Check (over Lesson 10–5) CCSS Then/Now 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 Lesson Menu

Determine whether BC is tangent to the given circle. ___ A. yes B. no 5-Minute Check 1

Determine whether BC is tangent to the given circle. ___ A. yes B. no 5-Minute Check 1

Determine whether QR is tangent to the given circle. ___ A. yes B. no 5-Minute Check 2

Determine whether QR is tangent to the given circle. ___ A. yes B. no 5-Minute Check 2

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

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

Find x. Assume that segments that appear to be tangent are tangent. C. 20 D. 5-Minute Check 4

Find x. Assume that segments that appear to be tangent are tangent. C. 20 D. 5-Minute Check 4

SL and SK are tangent to the circle. Find x. ___ A. 1 B. C. 5 D. 44 __ 5 2 5-Minute Check 5

SL and SK are tangent to the circle. Find x. ___ A. 1 B. C. 5 D. 44 __ 5 2 5-Minute Check 5

Mathematical Practices Content Standards Reinforcement of G.C.4 Construct a tangent line from a point outside a given circle to the circle. Mathematical Practices 3 Construct viable arguments and critique the reasoning of others. 1 Make sense of problems and persevere in solving them. CCSS

You found measures of segments formed by tangents to a circle. Find measures of angles formed by lines intersecting on or inside a circle. Find measures of angles formed by lines intersecting outside the circle. Then/Now

secant Vocabulary

Concept

A. Find x. Theorem 10.12 Substitution Simplify. Answer: Use Intersecting Chords or Secants A. Find x. Theorem 10.12 Substitution Simplify. Answer: Example 1

A. Find x. Theorem 10.12 Substitution Simplify. Answer: x = 82 Use Intersecting Chords or Secants A. Find x. Theorem 10.12 Substitution Simplify. Answer: x = 82 Example 1

B. Find x. Step 1 Find mVZW. Theorem 10.12 Substitution Simplify. Use Intersecting Chords or Secants B. Find x. Step 1 Find mVZW. Theorem 10.12 Substitution Simplify. Example 1

mWZX = 180 – mVZW Definition of supplementary angles Use Intersecting Chords or Secants Step 2 Find mWZX. mWZX = 180 – mVZW Definition of supplementary angles x = 180 – 79 Substitution x = 101 Simplify. Answer: Example 1

mWZX = 180 – mVZW Definition of supplementary angles Use Intersecting Chords or Secants Step 2 Find mWZX. mWZX = 180 – mVZW Definition of supplementary angles x = 180 – 79 Substitution x = 101 Simplify. Answer: x = 101 Example 1

Subtract 25 from each side. Use Intersecting Chords or Secants C. Find x. Theorem 10.12 Substitution Multiply each side by 2. Subtract 25 from each side. Answer: Example 1

Subtract 25 from each side. 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 Example 1

A. Find x. A. 92 B. 95 C. 98 D. 104 Example 1

A. Find x. A. 92 B. 95 C. 98 D. 104 Example 1

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

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

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

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

Concept

Substitute and simplify. Use Intersecting Secants and Tangents A. Find mQPS. Theorem 10.13 Substitute and simplify. Answer: Example 2

Substitute and simplify. Use Intersecting Secants and Tangents A. Find mQPS. Theorem 10.13 Substitute and simplify. Answer: mQPS = 125 Example 2

B. Theorem 10.13 Substitution Multiply each side by 2. Answer: Use Intersecting Secants and Tangents B. Theorem 10.13 Substitution Multiply each side by 2. Answer: Example 2

B. Theorem 10.13 Substitution Multiply each side by 2. Answer: Use Intersecting Secants and Tangents B. Theorem 10.13 Substitution Multiply each side by 2. Answer: Example 2

A. Find mFGI. A. 98 B. 108 C. 112.5 D. 118.5 Example 2

A. Find mFGI. A. 98 B. 108 C. 112.5 D. 118.5 Example 2

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

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

Concept

A. Theorem 10.14 Substitution Multiply each side by 2. Use Tangents and Secants that Intersect Outside a Circle A. Theorem 10.14 Substitution Multiply each side by 2. Example 3

Subtract 141 from each side. Use Tangents and Secants that Intersect Outside a Circle Subtract 141 from each side. Multiply each side by –1. Example 3

Subtract 141 from each side. Use Tangents and Secants that Intersect Outside a Circle Subtract 141 from each side. Multiply each side by –1. Example 3

B. Theorem 10.14 Substitution Multiply each side by 2. Use Tangents and Secants that Intersect Outside a Circle B. Theorem 10.14 Substitution Multiply each side by 2. Example 3

Use Tangents and Secants that Intersect Outside a Circle Add 140 to each side. Example 3

Use Tangents and Secants that Intersect Outside a Circle Add 140 to each side. Example 3

A. A. 23 B. 26 C. 29 D. 32 Example 3

A. A. 23 B. 26 C. 29 D. 32 Example 3

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

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

Theorem 10.14 Substitution Apply Properties of Intersecting Secants Example 4

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

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

A. 25 B. 35 C. 40 D. 45 Example 4

A. 25 B. 35 C. 40 D. 45 Example 4

Concept

End of the Lesson