Lesson 1

Lines, Angles, and Curves

Students begin this lesson by discussing what they notice and wonder about several images of circles that contain different kinds of line segments. Then, they are introduced to the vocabulary terms chord (a segment whose endpoints are on a circle), central angle (an angle formed by 2 rays whose endpoints are the center of the same circle), and arc (the portion of a circle between 2 endpoints). Students write definitions of these terms based on examples and non-examples. Then, they prove a property of congruent chords.

The definitions developed in this lesson are foundational for the rest of the unit. For example, students will use their knowledge of chords when analyzing inscribed angles. They’ll use central angle measurements to find areas of sectors and lengths of arcs, and they will define the radian measure of a central angle as the ratio of the length of the arc it defines to the radius of the circle.

Students attend to precision (MP6) as they write careful definitions of vocabulary terms.

Comprehend (in spoken and written language) the definitions of chord, arc, and central angle.

Let’s define some line segments and angles related to circles.

I know what chords, arcs, and central angles are.

Building On

HSG-CO.A.1

Addressing

Building Towards

HSG-C.A.2

arc

The part of a circle lying between two points on the circle.
central angle

An angle formed by two rays whose endpoints are the center of a circle.
chord

A chord of a circle is a line segment both of whose endpoints are on the circle.