5-Minute Check on Lesson 10-3
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Transcript of 5-Minute Check on Lesson 10-3
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5-Minute Check on Lesson 10-35-Minute Check on Lesson 10-35-Minute Check on Lesson 10-35-Minute Check on Lesson 10-3 Transparency 10-4
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The radius of ⊙R is 35, LM NO, LM = 45 and mLM = 80.Find each measure.
1. m NO
2. m NQ
3. NO
4. NT
5. RT
6. Which congruence statement is true if RS and TU are congruent chords of ⊙V?Standardized Test Practice:
A CB DRS SU RS TU ST RU RS ST
45
80°
40°
22.5
26.81
B
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Lesson 10-4
Inscribed Angles
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Objectives
• Find measures of inscribed angles
• Find measures of angles of inscribed polygons
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Vocabulary
• Inscribed Angle – an angle with its vertex on the circle and chords as its sides
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Circles – Inscribed Anglesy
x
F
E
J
K
Inscribe A
ngles
-- M
easure Y
° = ½
X°
(central a
ngle)
Center
X°
Y°
Measure Y° = ½ measure Arc KEF
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In and Find the measures of the numbered angles.
First determine
Arc Addition Theorem
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Simplify.
Subtract 168 from each side.
Divide each side by 2.
So, m
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Answer:
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In and Find the measures of the numbered angles.
Answer:
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ALGEBRA Triangles TVU and TSU are inscribed in with Find the measure of each numbered angle if and
∆UVT and ∆ UST are right triangles. Since they intercept congruent arcs, then m1 = m2. The third angles of the triangles must also be congruent, so m2 = m4 .
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Angle Sum Theorem
Simplify.
Subtract 105 from each side.
Divide each side by 3.Use the value of x to find the measures of
Given
Given
Answer:
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Answer:
ALGEBRA Triangles MNO and MPO are inscribed in with Find the measure of each numbered angle if and
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Quadrilateral QRST is inscribed in If and Find and
Draw a sketch of this situation.
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To find we need to know
To find first find
Inscribed Angle Theorem
Sum of angles in circle = 360
Subtract 174 from each side.
Inscribed Angle Theorem
Substitution
Divide each side by 2.
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To find we need to know but first we must find
Inscribed Angle Theorem
Sum of angles in circle = 360
Subtract 204 from each side.
Inscribed Angle Theorem
Divide each side by 2.
Answer:
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Answer:
Quadrilateral BCDE is inscribed in If and find and
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Summary & Homework
• Summary:– The measure of the inscribed angle is half the
measure of its intercepted arc– The angles of inscribed polygons can be found by
using arc measures
• Homework: – pg 549-550; 7, 9,10, 15, 22-25