Download Section 11.4 Inscribed Polygons

Geometry – Chapter 11 Lesson Plans
Section 11.4 – Inscribed Polygons
Enduring Understandings: The student shall be able to:
1. Inscribe regular polygons in circles.
2. Explore the relationship between the length of a chord and its distance from the center
of the circle.
Standards:
30. Circles
Identifies and defines circles and their parts (center, arc, interior, exterior); segments and
lines associated with circles (chord, diameter, radius, tangent, secant); properties of circles
(congruent, concentric, tangent); relationship of polygons and circles (inscribed,
circumscribed); angles (central; inscribed; formed by tangents, chords, and secants).
31. Circles
Apples geometric relationships to solving problems, such as relationships between lines
and segments associated with circles, the angles they form, and the arcs they subtend; and
the measures of these arcs, angles, and segments.
Essential Questions: What is the relationship of the length of a chord and its distance from
the center of the circle?
Warm up/Opener:
Activities:
Circumscribed means to go around, and is done on the outside of something – like when a
person circumscribes the world. Inscribed is when something is inside something..
A circle circumscribes a polygon when it goes around the outside of the polygon.
A polygon is inscribed in the circle if the polygon is inside of the circle.
Definition: A polygon is inscribed in a circle iff every vertex of the polygon lies on the circle.
Have class inscribe a square inside a circle. Then have the class inscribe a hexagon and then
construct the perpendicular bisectors to find the center.
What can we say about the centers of the inscribed polygons and the respective circles? The
center of the inscribed polygon and the center of the circle are congruent.
This activity suggests the following theorem:
Thm. 11.6: In a circle or in congruent circles, two chords are congruent iff they are
equidistant from the center.
This can be shown to be true via the Pythagorean Theorem.
Assessments: Do the “Check for Understanding” 1, 2, 4, 5
CW WS 11-4 of the blue book.
HW pg 476-477, # 9 - 25 odd (9) – assigned 9 – 17 odd (5)