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Lesson Menu Five-Minute Check (over Lesson 10–5) Then/Now New Vocabulary Theorem Example 1:Use Intersecting Chords or Secants Theorem Example 2:Use Intersecting Secants and Tangents Theorem 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

Over Lesson 10–5 5-Minute Check 1 A.yes B.no Determine whether BC is tangent to the given circle. ___

Over Lesson 10–5 5-Minute Check 2 A.yes B.no Determine whether QR is tangent to the given circle. ___

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

Over Lesson 10–5 5-Minute Check 4 Find x. Assume that segments that appear to be tangent are tangent. A. B. C.20 D.

Over Lesson 10–5 5-Minute Check 5 SL and SK are tangent to the circle. Find x. ___ A.1 B. C.5 D.44 __ 5 2

Then/Now You found measures of segments formed by tangents to a circle. (Lesson 10–5) Find measures of angles formed by lines intersecting on or inside a circle. Find measures of angles formed by lines intersecting outside the circle.

Vocabulary secant

Concept

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

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

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

C. Find x. Theorem Substitution Multiply each side by 2. Example 1 Use Intersecting Chords or Secants Subtract 25 from each side. Answer: x = 95

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

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

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

Concept

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

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

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

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

Concept

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

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

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

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

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

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

Example 4 Apply Properties of Intersecting Secants Theorem Substitution

Example 4 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

Concept

End of the Lesson