today in geometry… review: finding inside and outside angles of circles warm up: finding angles ...
TRANSCRIPT
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TODAY IN GEOMETRY…
Review: Finding inside and outside angles of circles
Warm up: Finding angles
Learning Target : 10.6 You will find lengths of segments in a circle
Independent practice
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REVIEW: So far we have learned to find ANGLES of the following circles and intersecting lines.
𝑥
𝑥
𝑥
𝑥
INSIDE ANGLE:
OUTSIDE ANGLE:
INSCRIBED ARC:
MINOR ARC:
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REVIEW: Solve for x.
𝑥
36 °126 °
𝑥 142 °118°
2 𝑥+6
4 𝑥−6
∙22 ∙
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We reviewed how to find ANGLES of intersecting lines and circles.
NOW…we will find LENGTHS of segments of intersecting lines and
circles!
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SEGMENTS OF A CHORD THEOREM: The products of segments of two intersecting chords are equal.
𝑐
𝑎𝑑
𝑏𝑎 ∙𝑏¿𝑐 ∙𝑑
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EXAMPLE: Find x.
Use Segments of a Chord Theorem Multiply
Divide
8 96
𝑥
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PRACTICE: Find x.
Use Segments of a Chord Theorem Multiply
Divide
8 4
14𝑥
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EXAMPLE: Find x.
Use Segments of a Chord Theorem Distribute
Subtract
Subtract
Divide
3 5
𝑥+1 𝑥+7
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PRACTICE: Find x.
Use Segments of a Chord Theorem Distribute
Subtract
Subtract
Divide
78
2 𝑥+43 𝑥+1
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SEGMENTS OF SECANTS THEOREM: The product of one of the whole segment and the exterior segment of the secant is equal to the product of the other whole segment and the exterior segment of the secant.
𝑑𝑐
𝑎
𝑏
𝐸
𝑎 ∙(𝑎+𝑏)¿𝑐 ∙(𝑐+𝑑)
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EXAMPLE: Find x.
Use Segments of a Secant Theorem Distribute and Simplify
Multiply Subtract
Divide
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PRACTICE:
Use Segments of Secants Theorem Distribute and Simplify
Multiply Subtract
Divide
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EXAMPLE: Find x.
Use Segments of a Secant Theorem Combine like terms
Distribute Subtract
Subtract
Divide
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EXAMPLE: Find x.
Use Segments of a Secant Theorem Combine like terms
Distribute Subtract
Subtract
Divide
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SEGMENTS OF SECANTS AND TANGENTS: The square of the segment of the tangent is equal to the product of the whole segment and the exterior segment of the secant.
𝑐𝑏
𝑎
𝐸
𝑎2¿𝑏 ∙(𝑏+𝑐)
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EXAMPLE: Find x.
Use Segments of a Secant & Tangents Square and Distribute
Subtract
Divide
𝑥8
16
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EXAMPLE: Find x.
Use Segments of a Secant & Tangents Square and Distribute
Subtract
Divide
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EXAMPLE: Find x.
Use Segments of a Secant & Tangents Add and Multiply
Square root
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PRACTICE: Find x.
Use Segments of a Secant & Tangents Add and Multiply
Square root
𝑥
214
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EXAMPLE: Find x.
Use Segments of a Secant & Tangents Distribute
FOIL Subtract
Subtract
Divide
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PRACTICE: Find x.
Use Segments of a Secant & Tangents Distribute
FOIL Subtract
Subtract
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HOMEWORK #6:
Pg. 692: 3, 4, 6, 9-14
If finished, work on other assignments:
HW #1: Pg. 655: 3-20, 24-26, 30HW #2: Pg. 661: 3-14, 17, 23HW #3: Pg. 667: 3-15HW #4: Pg. 676: 3-16 Pg. 679: 40-46HW #5: Pg. 683: 3-13