  Master the 7 pillars of school success

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.

### 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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