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G.C.1 Prove that all circles are similar

G.C.2 Identify and describe relationships among inscribed angles, radii, and chords. Include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle.

G.C.3 Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle.

G.C.4 (+) Construct a tangent line from a point outside a given circle to the circle.

Inscribed Angles

Inscribed Angles

More Chords

Chords

Arcs and Angles

Central Angles

Tangents

Geometry Vocabulary

Circles: Tangents,Secants,Chords

Lesson 1: Circles-

Geometry Vocabulary

 

Introduction to the Geometry Vocabulary

Circle defined and illustrated

Radius defined and illustrated

Chord defined and illustrated

Diameter defined and illustrated

Secant defined and illustrated

Tangent defined and illustrated

Is the line, ray, or segment best described as a radius, chord, diameter, secant or tangent of the circle?

Explanation of Circle theorem that states: In a plane a line is tangent to the circle, if and only if, it is perpendicular to the radius of the circle at its endpoint

 

 

Lesson 2: Tangents and Circles

Concentric circles defined and illustrated

Externally tangent circles defined and illustrated

Internally tangent circles defined and illustrated

Common internal tangents defined and illustrated

Common external tangents defined and illustrated

Pictures of internally tangent circles, and common externally tangent circles

Tangent theorem number 2 explained and illustrated

 

 

Lesson 3: Circles - Central angles, arc measures, major and minor arcs

Central angle defined and illustrated

Minor arc of a circle defined and illustrated

Semicircle defined and illustrated

Major arc defined and illustrated

Identify the given arc as a minor arc, major arc, or semicircle

Sample problems finding the measure of an arc

 

 

Lesson 4: Circles - Arcs and Angles

Rules for naming a circle

Naming a radius and which symbols to use

Naming a central angle

Sample problem finding the angle measure inside a circle The solution involves using vertical angles

Sample problem finding the angle measure inside a circle. The solution to this problem involves using a diameter in order to find the angle measure

Sample problem finding an arc measure. The solution is found using the central angle.

Sample problem finding an arc measure

Sample problem involving finding an arc measure

Rules for finding the major arc

Find the angle measure

 

 

Lesson 5: Chords on a Circle

Chords Theorem 1: In congruent circles two minor arcs are congruent if and only if their corresponding chords are congruent explained and illustrated

Practice problems using chords theorem 1

Theorem 2 explained and illustrated. If one chord is a perpendicular bisector of another chord then the first chord is a diameter

Theorem 2 Illustrated with a fold-able

Theorem 3 Explained and Illustrated If a diameter of a circle is perpendicular to a chord then the diameter intersects the chord and its arc

Practice problems involving Chord Theorem 3

Theorem 4 In the same circle, two chords are congruent if and only if they are an equal distance from the center

 

 

Lesson 6: More Chords on a Circle

Problem 19 Find the angle measure of M and N

This problem involves using two congruent arcs in order to find an angle measure

Second problem involving finding angle measure with two congruent arcs

Problem 3 Involves two perpendicular chords and trying to find the measure of an arc

Matching problems involving arcs and chords

Sample problem involving trying to find the measure of an arc using two congruent arcs and two congruent chords.

 

 

Lesson 7: Inscribed Angles of a circle

Description of where the vertex is in an inscribed angle

Definition and illustration of an inscribed angle

Definition and illustration of an intercepted arc

Definition and illustration of an inscribed polygon

Definition and an illustration of a circumscribed circle

Inscribed angle and it's measure theorem explained

Inscribed angles that intercept theorem explained

Sample problem involving finding an arc measure when given angle measures.

Sample problem finding the arc measure

Sample problem finding an inscribed angle measure worked out

 

 

Lesson 8: Inscribed angles and angles outside the circle

Central angle and arc measures defined and illustrated

Inscribed angles and angles with the vertex on the circle defined and illustrated

Definition and explanation along with an illustration of an angle inside the circle but not central

Sample problem- Finding the measure of an inside angle given two arc measures.

Angles outside a circle defined and illustrated

Formula for finding the measure angle of an angle outside the circle

Helpful hint for when to add and when to subtract the inside and outside arcs

Sample problem finding the arc measure with step by step directions

Sample problem- finding the arc measure

 

 

Lesson 9: Inscribed angles problems

Review of the diagram. During the review the diameter of the circle, point of tangency, and several arcs are identified.

The goal of the activity is to identify ten angles drawn inside and outside the circle.

Sample problem involving an inscribed angle

The remaining video works ten angles inside and outside of the circle

 

 

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Check the Table of Contents for a list of all of the topics covered.
Circles Unit. The unit contains 17 lessons. Here is a list of the Common Core Standards covered within this Unit.