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Splash Screen. Five-Minute Check (over Lesson 10–5) NGSSS 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 - PowerPoint PPT PresentationTRANSCRIPT
Five-Minute Check (over Lesson 10–5)
NGSSS
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
Over Lesson 10–5
A. yes
B. no
Determine whether BC is tangent to the given circle.___
A. A
B. B
A B
0%0%
Over Lesson 10–5
A. yes
B. no
Determine whether QR is tangent to the given circle.___
A. A
B. B
A B
0%0%
Over Lesson 10–5
A. A
B. B
C. C
D. D A B C D
0% 0%0%0%
A. 10
B. 11
C. 12
D. 13
Find x. Assume that segments that appear to be tangent are tangent.
Over Lesson 10–5
A. A
B. B
C. C
D. D A B C D
0% 0%0%0%
Find x. Assume that segments that appear to be tangent are tangent.
A.
B.
C. 20
D.
Over Lesson 10–5
A. A
B. B
C. C
D. D A B C D
0% 0%0%0%
SL and SK are tangent to the circle. Find x.______
A. 1
B.
C. 5
D. 44
__5
2
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.
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.
Use Intersecting Chords or Secants
A. Find x.
Theorem 10.12
Substitution
Simplify.
Answer: x = 82
Use Intersecting Chords or Secants
B. Find x.
Theorem 10.12
Substitution
Simplify.
Step 1 Find mVZW.
Use Intersecting Chords or Secants
Step 2 Find mWZX.
WZX = 180 – VZW Definition of supplementaryangles
x = 180 – 79 Substitution
x = 101 Simplify.
Answer: x = 101
C. Find x.
Theorem 10.12
Substitution
Multiply each side by 2.
Use Intersecting Chords or Secants
Subtract 25 from each side.
Answer: x = 95
A. A
B. B
C. C
D. D A B C D
0% 0%0%0%
A. 92
B. 95
C. 98
D. 104
A. Find x.
A. A
B. B
C. C
D. D A B C D
0% 0%0%0%
A. 92
B. 95
C. 97
D. 102
B. Find x.
A. A
B. B
C. C
D. D A B C D
0% 0%0%0%
A. 96
B. 99
C. 101
D. 104
C. Find x.
Use Intersecting Secants and Tangents
A. Find mQPS.
Theorem 10.13
Substitute and simplify.
Answer: mQPS = 125
B.
Theorem 10.13
Use Intersecting Secants and Tangents
Substitution
Multiply each side by 2.
Answer:
A. A
B. B
C. C
D. D A B C D
0% 0%0%0%
A. 98
B. 108
C. 112.5
D. 118.5
A. Find mFGI.
A. A
B. B
C. C
D. D A B C D
0% 0%0%0%
A. 99
B. 148.5
C. 162
D. 198
B.
Use Tangents and Secants that Intersect Outside a Circle
A.
Theorem 10.14
Substitution
Multiply each side by 2.
Use Tangents and Secants that Intersect Outside a Circle
Subtract 141 from each side.
Multiply each side by –1.
Use Tangents and Secants that Intersect Outside a Circle
B.
Theorem 10.14
Substitution
Multiply each side by 2.
Use Tangents and Secants that Intersect Outside a Circle
Add 140 to each side.
A. A
B. B
C. C
D. D A B C D
0% 0%0%0%
A. 23
B. 26
C. 29
D. 32
A.
A. A
B. B
C. C
D. D A B C D
0% 0%0%0%
A. 194
B. 202
C. 210
D. 230
B.
Apply Properties of Intersecting Secants
Theorem 10.14
Substitution
Apply Properties of Intersecting Secants
Multiply each side by 2.
Subtract 96 from each side.
Multiply each side by –1.
A. A
B. B
C. C
D. D A B C D
0% 0%0%0%
A. 25
B. 35
C. 40
D. 45