Aim #18: How can we work with the properties of tangents ...
The Bronx High School of Science Math Department
Valerie Reidy, Principal R. Jahoda, A.P.
Name:_______________________________ Date:____________ Period:________
M4 Teacher: Ms. Zinn
Formulas for Determining Angle Measures
(use p377 of the Amsco Review Book to help you)
|Type of Angle |Identifying Elements |Diagram |Formula |
|Central Angle | |[pic] | |
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|Inscribed angle | | | |
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|Angle formed by a tangent and a chord| | | |
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|Angle formed by a secant and a chord | | | |
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|Angle formed by two chords | | | |
|intersecting within a circle | | | |
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|Angle formed by a tangent and a | | | |
|radius | | | |
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|Type of Angle |Identifying Elements |Diagram |Formula |
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|Angle formed by two secants | | | |
|intersecting outside the circle | | | |
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|Angle formed by a secant and a tangent| | | |
|intersecting outside the circle | | | |
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|Angle formed by two tangent | | | |
|intersecting outside of the circle | | | |
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[pic]
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Some theorems used in Circle proofs:
1) In a circle, all radii are congruent.
2) In a circle, if two central angles are congruent, then their intercepted arcs are congruent.
3) In a circle, if two chords are congruent, then the arcs they intercept are congruent
4) In a circle, if two arcs are congruent, then the chords that form them are congruent.
5) If a radius (diameter) is perpendicular to a chord, then it bisects the chord and its arcs.
6) In a circle, if two chords are congruent, then they are equidistant from the center of the circle.
7) If an angle is inscribed in a semicircle, then it is a right angle.
8) If two inscribed angles intercept the same arc, then they are congruent.
9) If two chords in a circle are parallel, then they intercept congruent arcs between them.
10) If a line is tangent to a circle, then it is perpendicular to the radius at that point.
11) If two tangent segments are drawn to a circle from an external point, they are congruent.
THESE ARE NOT ALL OF THE THEOREMS WE HAVE SPOKEN ABOUT!
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