SECTION 8.2B (PART 2)ANGLE PROPERTIES IN A CIRCLE
REVIEW: CIRCLE PROPERTIES #1 AND #2
Isosceles Triangle
Compl. Angles
Isosceles Triangle
Property #1: Angles inscribed by a diameter is equal to 90°
Property #2: Chords of equal length will contain central angles of equal value
Use the properties to find the value of the missing angles
Note: Two radii in a circle will create an isosceles triangle
Property #3) Inscribed angles “containing” the same(equal)chords or arcs have the same angles (Rabbit Ears)
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If two chords have the same length
The angles they contain will be equal
PRACTICE: FIND THE MISSING ANGLES
Both contain arc BC
Both contain chord AD
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Both contain chord BC
BD = BC
Both contain arc AD
4. The inscribed angle is equal to half of the central angleif they “contain” the same chord or arc
Central Angle Applet
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Find the value of the “x”, “y”, and “z”
Angle AOB is a central Angle
“x” and “y” are both inscribed angles
“z” is part of an isosceles triangle
In a situation when the two radii’sare moved past the center of thecircle, the Central angle will be theouter angle AOB
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I) PROVING ANGLE PROPERTIES:
CHALLENGE : FIND THE MISSING ANGLES
Both contain arc CD
Central angle is doublethe inscribed angle
Central angle is doublethe inscribed angle
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Given:
All inscribed angles from the same(equal)chord must be the same
Rabbit Ears!!