Outline
Circles (C) Cluster
MAFS.912.G-C.1.1 Prove that all circles are similar.
MAFS.912.G-C.1.2 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.
MAFS.912.G-C.1.3 Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle.
MAFS.912.G-C.2.5 Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector.
Table of Contents
MAFS.912.G-C.1.1
MAFS.912.G-C.1.2
- Circle Terminology
- Circle Tangent-Types Illustrator
- Properties of Tangents Drawn to Circles (A)
- Properties of Tangents Drawn to Circles (B)
- Animation 3
- Tangents to Circles: Investigation
- Where to Sit? (I)
- Where to Sit (II)?
- Inscribed Angle Theorem (V1)
- Animation 12
- Inscribed Angle Theorem: Take 2!
- Inscribed Angle Theorems: Take 3!
- Proof Exercise: Inscribed Angle Theorem (Case 1)
- Proof Exercise: Inscribed Angle Theorem (Case 2)
- Proof Exercise: Inscribed Angle Theorem (Case 3)
- Inscribed Angle Theorems: Take 4!
- Inscribed Angle Theorem: Corollary 1
- Animation 20 (Inscribed Angle Dance!)
- Thales' Theorem (VA)
- Animation 116
- Thales' Theorem (VB)
- Animation 54
- Angle Formed by Chord & Tangent (I)
- Animation 50
- Angle Formed by Chord & Tangent (II)
- Animation 78
- Congruent Chords: Quick Investigation
- Congruent Chords (I)
- Animation 76
- Diameters & Chords I (VA)
- Diameters & Chords I (VB)
- Animation 24
- Congruent Chords Action (A)
- Animation 96
- Equidistant Chord Action
- Animation 101
- Angle Formed by 2 Chords (I)
- Animation 32
- Angle Formed by 2 Chords (II)
- Animation 33
- Angles from Secants and Tangents (V1)
- Animation 61
- Angle From 2 Secants (V2)
- Animation 45
- Crossing Chords: Proof Hint
- Animation 79
- Crossing Chords Property & Proof Start
- Crossing Chords Property & Proof Start (II)
- Secants: Proof Hint
- Animation 88
- Animation 92
MAFS.912.G-C.1.3
MAFS.912.G-C.2.5