Download Standards Framework Template

Understand and apply theorems about circles
Grade:
Common Core/Essential
Standard #:
G.C.3
Course:
Description:
Construct the inscribed and circumscribed
circles of a triangle, and prove properties of
angles for a quadrilateral inscribed in a circle.
Learning Targets:
I can define the terms inscribed, circumscribed, angle
bisector, and perpendicular bisector. (K)
I can construct the inscribed circle whose center is the
point of intersection of the angle bisectors (the
incenter).(P)
I can construct the circumscribed circle whose center
is the point of intersection of the perpendicular
bisectors of each side of the triangle (the
circumcenter)(P)
I can apply the Arc Addition Postulate to solve for
missing arc measures. (S)
I can prove that opposite angles in an inscribed
quadrilateral are supplementary. (R)
Essential Terminology:
Inscribed, circumscribed, angle bisector, perpendicular
bisector, construction, compass, straightedge,
intersection, incenter, circle, circumcenter,
quadrilateral, arc, inscribed angle, Arc Addition
Postulate, equation, opposite angles, supplementary
Unit:
Instructional Days:
Recommended Resources:
Prentice Hall – Common Core State Standards
Phschool.com: Homework Tutorial Videos, Quizzes
Prentice Hall Geometry – Chapter 5
Tenmarks.com
Online (only links specific to this standard):
Phschool.com: Homework Tutorial Videos, Quizzes
Tenmarks.com
Essential Readings:
Prentice Hall Geometry – page 249 – 251, 256 - 259
Enduring Understandings:
The properties of polygons, lines, and angles can be used to understand circles; the properties of circles can be used
to solve problems involving polygons, lines, and angles.
Essential Question:
How can the properties of circles, polygons, lines and angles be useful when solving geometric problems?
Understand and apply theorems about circles
Activating Strategy:
Teacher will instruct and model the concepts of the perpendicular and angle bisectors of a triangle. Teacher will
teach concurrent lines, medians, and altitudes. The students will learn the points of concurrency for perpendicular
bisectors, angle bisectors, altitudes, and medians.
Paper Folding Activity in Prentice Hall Geometry – page 256
Suggested Instructional Tasks:
Teacher can use construction to show the points of concurrency and how they
Literacy Component: Reading
Prentice Hall Geometry – page 249 – 251, 256 -259
Writing
Explain the four different lines of concurrency and the
special points that correlate to the lines. State the special
characteristic of the centroid, circumcenter, and incenter.
Summarizing Strategy:
Support for Differentiation:
ELL
EC
Sample Formative Assessment (aligned to Learning Target):
AIG