Lesson 3 - Properties of Angles and...
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Lesson 3 Properties of Angles and Circles.notebook February 05, 2015 Outcomes Shape & Space (Unit 1, 7/8) Measurement 1. Solve problems and jusfy the soluon strategy, using the following circle properes: • the perpendicular from the centre of a circle to a chord bisects the chord • the measure of the central angle is equal to twice the measure of the inscribed angle subtended by the same arc • the inscribed angles subtended by the same arc are congruent • a tangent to a circle is perpendicular to the radius at the point of tangency. Review Your Skills!
Transcript of Lesson 3 - Properties of Angles and...
Lesson 3 Properties of Angles and Circles.notebook February 05, 2015
OutcomesShape & Space (Unit 1, 7/8)
Measurement
1. Solve problems and jusfy the soluon strategy, using the following circle properes:
• the perpendicular from the centre of a circle to a chord bisects the chord
• the measure of the central angle is equal to twice the measure of the inscribed angle subtended by the same arc
• the inscribed angles subtended by the same arc are congruent
• a tangent to a circle is perpendicular to the radius at the point of tangency.
Review Your Skills!
Lesson 3 Properties of Angles and Circles.notebook February 05, 2015
An arc is a portion of the circumference of the circle.
Lesson 3 Properties of Angles and Circles.notebook February 05, 2015
A minor arc is an arc that goes less than 1/2 way around the circle
A major arc is an arc that goes more than 1/2 way around the circle
Note that when you are talking about an arc in a circle, you must state whether it is the minor arc or the major arc
A
B
Otherwise in the above picture, if we just said arc AB, how would we know if we are talking about the red portion of the circle or the blue portion.
An inscribed angle is an angle that is formed by two chords
Inscribed Angle ABCA
B
C
Chord AB
Chord BC
A
B
C
Chord AB
Chord BC
The sentence an inscribed angle subtended by an arc, means that the angle formed by two chords is connected by an arc.
Lesson 3 Properties of Angles and Circles.notebook February 05, 2015
The central angle is the angle formed by joining the endpoints of an arc with the centre of the circle
Red = Inscribed Angle, Blue = Central Angle
Properties
What this means...
Centre Angle = 2x Inscribed Angle
Inscribed Angle = 1/2 Centre Angle
Lesson 3 Properties of Angles and Circles.notebook February 05, 2015
Try These! #1 Explains the Property Properties
What this means...
If you move a point along the Major arc,
the angles of the inscribed angle always stay the same as long as the chord stays the same
Lesson 3 Properties of Angles and Circles.notebook February 05, 2015
Solve for the Unknown Angles x and y
Practice Your Skills
Pg 410 412
Everybody: 3, 4acd 5 ac
Feeling Lucky? #13
Properties
Lesson 3 Properties of Angles and Circles.notebook February 05, 2015
What this means...
If the chord is the diameter, the angle is 90 degrees
This applies to the first rule, where the central angle is double the inscribed angle.
Solve for the Unknown Angles x and y
Lesson 3 Properties of Angles and Circles.notebook February 05, 2015
Practice Your Skills
Pg 410 412
Everybody: 4b, 5b, 6, 11
Feeling Lucky? #15
Review Your Skills!
