the rules of circle theorems 1 · pdf filecircle theorems are important in real life. ... the...
TRANSCRIPT
Review Some of these rules are related to each other. Can you see how they might be?
These are the Rules ofCircle Theorems
The Rules of Circle Theorems 1
littlestreams.co.uk - © 2015 LittleStreams Ltd. - Resource Ref No. MATP_GEO_CIR02_UK
Theorem 1The angle at the centre is always twice the angle at the circumference
Circle theorems are important in real life. They are used to construct circles without knowing where the centre is. Can you work out how?
Theorem 2The angle at the circumference in a semi-circle is always 90˚
90˚
180˚
Theorem 3Angles within the same segment are always equal
Minor Segment
Major Segment
ab
Theorem 4Opposite angles in a quadrilateral add up to 180˚
a
b
a + b = 180˚
a = b
a
b
b = 2a
Theorem 7The angle (a) between the tangent and the chord at the point of contact is equal to the angle (b) in the alternate segment
Review Some of these rules are related to each other. Can you see how they might be?
The Rules of Circle Theorems 2
littlestreams.co.uk - © 2015 LittleStreams Ltd. - Resource Ref No. MATP_GEO_CIR03_UK
Theorem 5The lengths of the two tangents from a point to a circle are always equal
90˚
Theorem 8A perpendicular line from a chord through the centre bisects the chord
a
bc
ab = ac
Theorem 6The angle between a tangent and the radius is always 90˚
a
90˚
a
c
ab = bc
90˚
b
b
a = b
90˚
Radius
Tangent
PerpendicularA line drawn an angle of exactly 90 degreees compared to another line
BisectTo divide a line into two equal halves
Important Words...
Chord
Tangent
Review Some of these rules are related to each other. Can you see how they might be?
These are the Rules ofCircle Theorems
The Rules of Circle Theorems 1
little-streams.com - © 2015 LittleStreams Ltd. - Resource Ref No. MATP_GEO_CIR02_US
Theorem 1The angle at the center is always twice the angle at the circumference
Circle theorems are important in real life. They are used to construct circles without knowing where the center is. Can you work out how?
Theorem 2The angle at the circumference in a semi-circle is always 90˚
90˚
180˚
Theorem 3Angles within the same segment are always equal
Minor Segment
Major Segment
ab
Theorem 4Opposite angles in a quadrilateral add up to 180˚
a
b
a + b = 180˚
a = b
a
b
b = 2a
Theorem 7The angle (a) between the tangent and the chord at the point of contact is equal to the angle (b) in the alternate segment
Review Some of these rules are related to each other. Can you see how they might be?
The Rules of Circle Theorems 2
little-streams.com - © 2015 LittleStreams Ltd. - Resource Ref No. MATP_GEO_CIR03_US
Theorem 5The lengths of the two tangents from a point to a circle are always equal
90˚
Theorem 8A perpendicular line from a chord through the center bisects the chord
a
bc
ab = ac
Theorem 6The angle between a tangent and the radius is always 90˚
a
90˚
a
c
ab = bc
90˚
b
b
a = b
90˚
Radius
Tangent
PerpendicularA line drawn an angle of exactly 90 degreees compared to another line
BisectTo divide a line into two equal halves
Important Words...
Chord
Tangent
Poster Variation Note for UK and US
Teachers’ Note
little-streams.com © 2015 LittleStreams Ltd. All Rights Reserved.
This PDF document contains Posters in both UK and US variations. The reason for this is to cater for alternate spellings that are required for each territory.
The UK and US variations are shown at the bottom of each page. The product code will end in either ‘US’ or ‘UK’. This is so you can print only the pages that are right for you.
Thank you for reading, and enjoy your Free Mathematics Poster!
LittleStreams
little-streams.com © 2015 LittleStreams Ltd. All Rights Reserved.
facebook.com/littlestreamspinterest.com/littlestreamstwitter.com/littlestreams
• Low Ink Usage• Clear and Concise• PDF Format• Full Rule Sets• Easily Prepared• Wide Range of Subjects• Available in Discounted
Bundles or for Individual Purchase.
• Buy and Keep Forever
Because you downloaded this, you might be interested in these...
Check out our Online Store to see all of these Card Game Bundles!