Unit 7, Lesson 5
Lines, Angles, and Curves
Integrated Math 2
5.1
Warm-up
What do you notice? What do you wonder?
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What do you notice? What do you wonder?
The images show some line segments that are chords and some segments that are not chords.
chords3 circles with lines inside each circle. First circle line extends on left side of circle. Middle circle line extends through the center point. Last circle line extends on right side of circle.
not chords3 circles with lines. First circle line segment is directly above circle. Middle circle line segment from center point to edge of circle. Last circle line segment from outside of circle, through circle and to other side of circle.
Write a definition of a chord.
The images show some highlighted objects that are arcs, and some highlighted objects that are not arcs.
arcs
not arcs
Write a definition of an arc.
The images show some angles that are central angles, and some that are not.
central angles3 circles with angles inside. First circle obtuse angle with circle center. Middle circle acute angle with circle center. Last circle straight line through center of circle.
not central angles3 circles with angles. First circle, acute angle with vertex on circle. Middle circle, obtuse angle inside circle. Last circle, angle on the exterior of circle.
Write a definition of a central angle.
The image shows a circle with 2 congruent chords.
Diameters and radii are two types of line segments that appear in circles. Here are some additional geometric objects associated with circles.
A chord is a line segment with both endpoints on a circle. A central angle in a circle is an angle whose vertex is at the center of the circle. An arc is a portion of a circle's circumference that is between two points on the circle. The measure of an arc is defined as the measure of the central angle formed by the radii drawn to the endpoints of the arc. For example, in the image, the highlighted arc between points and measures 45 degrees because the central angle measures 45 degrees.
chord
central angle $PQR$
arc ; ;
An arc is a part of a circle’s circumference between two points on the circle.
In this diagram, the blue highlighting shows one arc of the circle.
A central angle is an angle formed by two radii of a circle that each have an endpoint at the center of the circle.
In this diagram, the angle arc symbol shows one central angle of the circle.
A chord of a circle is a line segment with both endpoints on the circle.