In this Grade 7 Saxon Math Course 2 investigation, students learn to use a compass and straightedge to draw concentric circles and inscribe a regular hexagon and regular triangle in a circle. The lesson introduces key geometric vocabulary including arc, radius, pivot point, inscribed polygon, inscribed angle, chord, and diameter. Students practice hands-on construction techniques while exploring properties of regular polygons and circle geometry.
Section 1
📘 Properties of a Circle
The distance around a circle is its circumference. The distance from the center to a point on the circle is the radius. The distance across the circle through its center is the diameter, which equals two radii.
Next, you’ll use these concepts in hands-on activities. We'll practice drawing concentric circles, inscribing polygons, and dividing a circle into equal sectors using a compass.
Section 2
Concentric circles
Concentric circles are two or more circles that share a common center point but have different radii.
Think of a bull's-eye target or ripples from a pebble in a pond! They all share the exact same center point but get bigger with different radii, creating a cool nested effect. You draw them by keeping your compass pivot point fixed and just changing its width.
Section 3
Inscribed Polygon Definition & Regular Hexagon Construction
A polygon is inscribed in a circle if all of its vertices lie exactly on the edge of the circle, and all its interior space is inside the circle.
To construct a regular hexagon inscribed in a circle of radius , set your compass width to .
Mark a starting point on the circle, and "walk" the compass around the circumference to create six equally spaced intersection points.
Connecting these six points forms a regular hexagon.
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Section 1
📘 Properties of a Circle
The distance around a circle is its circumference. The distance from the center to a point on the circle is the radius. The distance across the circle through its center is the diameter, which equals two radii.
Next, you’ll use these concepts in hands-on activities. We'll practice drawing concentric circles, inscribing polygons, and dividing a circle into equal sectors using a compass.
Section 2
Concentric circles
Concentric circles are two or more circles that share a common center point but have different radii.
Think of a bull's-eye target or ripples from a pebble in a pond! They all share the exact same center point but get bigger with different radii, creating a cool nested effect. You draw them by keeping your compass pivot point fixed and just changing its width.
Section 3
Inscribed Polygon Definition & Regular Hexagon Construction
A polygon is inscribed in a circle if all of its vertices lie exactly on the edge of the circle, and all its interior space is inside the circle.
To construct a regular hexagon inscribed in a circle of radius , set your compass width to .
Mark a starting point on the circle, and "walk" the compass around the circumference to create six equally spaced intersection points.
Connecting these six points forms a regular hexagon.
Book overview
Jump across lessons in the current chapter without opening the full course modal.
Continue this chapter