Unit G: Circles (1.7, 6.1-6.3, 6.5-6.7)
□ I can define and identify parts of a circle.
□ I will identify and name parts of circle using appropriate notation.
□ I will sketch, label, and mark figures to match a given description.
□ I will find the measures of central angles and its intercepted arc.
□ I can use properties of tangents of circles to solve problems.
□ I will explain and use the relationship between a tangent and radius.
□ I will explain and use the relationship between tangent segments.
□ I can use properties of chords in a circle to solve problems.
□ I will explain and use the relationship between congruent chords and their intercepted arcs.
□ I will explain and use the relationship between chords, perpendicular bisectors, and the center of
the circle.
□ I can use properties of inscribed angles to solve problems.
□ I will calculate the measure of an inscribed angle and its intercepted arc.
□ I will explain and use the relationship between two inscribed angle that intercept the same arc.
□ I will explain and use the relationship formed by an angle inscribed in a semicircle.
□ I will explain and use the relationship between the angles of a cyclic quadrilateral.
□ I will explain and use the relationship formed by parallel lines in a circle.
□ I can use the formula for circumference of a circle.
□ I will explain the relationship between the circumference and diameter of a circle.
□ I will find the circumference of a circle given the radius or diameter.
□ I will find the diameter or radius of a circle given the circumference.
□ I will apply the formula for the circumference of a circle to solve word problems.
□ I can use the formula for the length of the arc of a circle.
□ I will find the length of an arc given the radius and arc measure.
□ I will find the radius of a circle given the arc length and arc measure.
□ I will find the measure of an arc given arc length and radius.
Key Vocabulary and Concepts
arc
arc length
arc measure
center
central angle
chord
circle
circumference
concentric circles
Conjectures
Tangent Conjecture
Tangent Segments Conjecture
Chord Central Angles Conjecture
congruent circles
cyclic quadrilateral
diameter
endpoints
externally tangent
inscribed angle
intercepted arc
internally tangent
major arc
minor arc
pi
point of tangency
radius
secant
semicircle
tangent
tangent circles
tangent segments
Chord Arcs Conjecture
Perpendicular to a Chord Conjecture
Chord Distance to Center Conjecture
Perpendicular Bisector of a Chord Conjecture
Inscribed Angle Conjecture
Inscribed Angles Intercepting Arcs Conjecture
Angles Inscribed in a Semicircle Conjecture
Online Textbook
http://math.kendallhunt.com
Cyclic Quadrilateral Conjecture
Parallel Lines Intercepted Arcs Conjecture
Circumference Conjecture
Arc Length Conjecture
classpass: bishop12
Online Resources
Overview of parts of a circle:
http://www.cliffsnotes.com/study_guide/Parts-of-Circles.topicArticleId-18851,articleId-18823.html
Information and Practice problems related to tangents to a circle:
http://www.mathwarehouse.com/geometry/circle/tangent-to-circle.php
Video and Practice Problems related to chords of a circle:
http://www.sophia.org/properties-of-chords-and-minor-arcs-in-congruent-circles--2/properties-of-chords-and-minor-arcs-incongruent-c--3-tutorial?pathway=geometry
Information and Practice problems related to inscribed angles:
http://www.mathwarehouse.com/geometry/circle/inscribed-angle.php
Video of problem involving inscribed angles: http://www.youtube.com/watch?v=-QBJtmEVg9s
Video of talking about difference of arc length and arc measure:
http://www.brightstorm.com/math/geometry/circles/arc-length/
Arc Length Calculator http://www.ajdesigner.com/phpcircle/circle_arc_length_s.php
Circumference and a Song:
http://www.mathwarehouse.com/geometry/circle/circumference-of-circle.php
Circle Tool Illustration of how radius, diameter and circumference relate:
http://illuminations.nctm.org/ActivityDetail.aspx?ID=116
Quick Overview of Circles and angles:
http://www.geometer.org/mathcircles/circles.pdf
Extension Exercises
Exploration of Spherical Geometry
http://www.mrlarkins.com/geometry/InteractiveTextbook/Ch03/03-03/PH_Geom_ch03-03_Ext.pdf
Circle and Triangle Proof (fairly tough Pythagorean Proof exercise)
http://gogeometry.com/problem/p099_circle_area_pythagoras.htm
Belt and Gear Problems and explanations
http://www.education.com/reference/article/firefighter-exam-study-guide-gear-belt-system/