lesson 4 menu 1.refer to the figure. the radius of is 35, = 80, lm = 45, and lm no. find. 2.find....
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1. Refer to the figure. The radius of is 35, = 80, LM = 45, and
LM NO. Find .
2. Find .
3. Find the measure of NO.
4. Find the measure of NT.
5. Find the measure of RT.
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• intercepted
• Find measures of inscribed angles.
• Find measures of angles of inscribed polygons.
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Measures of Inscribed Angles
Arc Addition Postulate
Simplify.
Subtract 168 from each side.
First determine
Divide each side by 2.
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Proof with Inscribed Angles
Proof:Statements Reasons
1. Given1.
2. 2. If 2 chords are , corr. minor arcs are .
4. 4. Inscribed angles of arcs are .
5. 5. Right angles are congruent.
6. ΔPJK ΔEHG 6. AAS
3. 3. Definition of intercepted arc
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Choose the best reason to complete the following proof.Given:
Prove: ΔCEM ΔHJM
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1. Given
2. ______
3. Vertical angles are congruent.
4. Radii of a circle are congruent.
5. ASA
Proof:Statements Reasons
1.
2.
3.
4.
5. ΔCEM ΔHJM
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1. A
2. B
3. C
4. D
A. Alternate Interior Angle Theorem
B. Substitution
C. Definition of angles
D. Inscribed angles of arcs are .
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Inscribed Arcs and Probability
The probability that is the same as the probability of L being contained in .
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Angles of an Inscribed Triangle
ΔUVT and ΔUVT are right triangles. m1 = m2 since they intercept congruent arcs. Then the third angles of the triangles are also congruent, so m3 = m4.
Angle Sum Theorem
Simplify.
Subtract 105 from each side.
Divide each side by 3.
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Angles of an Inscribed Triangle
Use the value of x to find the measures of
Given Given
Answer:
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Draw a sketch of this situation.
Angles of an Inscribed Quadrilateral
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Angles of an Inscribed Quadrilateral
To find we need to know
To find first find
Inscribed Angle Theorem
Sum of arcs in circle = 360
Subtract 174 from each side.
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Angles of an Inscribed Quadrilateral
Inscribed Angle Theorem
Substitution
Divide each side by 2.
Since we now know three angles of a quadrilateral, we can easily find the fourth.
mQ + mR + mS + mT = 360 360° in aquadrilateral
87 + 102 + 93 + mT = 360 Substitution
mT = 78 Subtraction
Answer: mS = 93; mT = 78