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10-4 Inscribed Angles
PROOF Write the specified type of proof.
22. two-column proof
Given:
Prove:
SOLUTION: Statements (Reasons):
1.
(Given)
2.
(Inscribed intercepting same arc are .)
3.
(Vertical
are .)
4.
(AA Similarity)
ALGEBRA Find each value.
23. x
SOLUTION: An inscribed angle of a triangle intercepts a diameter or semicircle if and only if the angle is a right angle. So,
The sum of the measures of the angles of a triangle is 180. So,
24. SOLUTION: An inscribed angle of a triangle intercepts a diameter or semicircle if and only if the angle is a right angle. So,
The sum of the measures of the angles of a triangle is 180. So,
Therefore,
25. x
SOLUTION: An inscribed angle of a triangle intercepts a diameter or semicircle if and only if the angle is a right angle. So,
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The sum of the measures of the angles of a triangle is 180. So,
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The sum of the measures of the angles of a triangle is 180. So,
10-4 Inscribed Angles
Therefore,
25. x
SOLUTION: An inscribed angle of a triangle intercepts a diameter or semicircle if and only if the angle is a right angle. So,
The sum of the measures of the angles of a triangle is 180. So,
26. SOLUTION: An inscribed angle of a triangle intercepts a diameter or semicircle if and only if the angle is a right angle. So,
The sum of the measures of the angles of a triangle is 180. So,
Therefore,
CCSS STRUCTURE Find each measure.
27. SOLUTION: If a quadrilateral is inscribed in a circle, then its opposite angles are supplementary.
Therefore,
28. SOLUTION: If a quadrilateral is inscribed in a circle, then its opposite angles are supplementary.
Therefore,
CCSS STRUCTURE Find each measure.
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29. SOLUTION: Page 2
10-4 Inscribed Angles
Therefore,
CCSS STRUCTURE Find each measure.
29. SOLUTION: If a quadrilateral is inscribed in a circle, then its opposite angles are supplementary.
Therefore,
30. SOLUTION: If a quadrilateral is inscribed in a circle, then its opposite angles are supplementary.
Therefore,
In
, FL = 24, HJ = 48, and
. Find each measure.
55. FG
SOLUTION: If a diameter (or radius) of a circle is perpendicular to a chord, then it bisects the chord and its arc. So,
Therefore, bisects 56. SOLUTION: If a diameter (or radius) of a circle is perpendicular to a chord, then it bisects the chord and its arc. So,
bisects Therefore, 57. NJ
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If a diameter (or radius) of a circle is perpendicular to a chord, then it bisects the chord and its arc. So,
Therefore, Page 3
bisects 56. SOLUTION: a diameterAngles
(or radius) of a circle is perpendicular to a chord, then it bisects the chord and its arc. So,
10-4IfInscribed
Therefore, bisects 57. NJ
SOLUTION: If a diameter (or radius) of a circle is perpendicular to a chord, then it bisects the chord and its arc. So,
bisects Therefore, 58. SOLUTION: If a diameter (or radius) of a circle is perpendicular to a chord, then it bisects the chord and its arc. So,
bisects Therefore, Find x.
59. SOLUTION: The sum of the measures of the central angles of a circle with no interior points in common is 360. So,
60. SOLUTION: The sum of the measures of the central angles of a circle with no interior points in common is 360. So,
61. SOLUTION: The sum of the measures of the central angles of a circle with no interior points in common is 360. So,
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SOLUTION: The sum of the measures of the central angles of a circle with no interior points in common is 360. So,
10-4 Inscribed Angles
61. SOLUTION: The sum of the measures of the central angles of a circle with no interior points in common is 360. So,
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