Download Topic VII Properties of Circles Opening routine What is the area of a

Topic VII Properties of Circles
Opening routine
What is the area of a circle with radius of 3 m?
Topic VII Properties of Circles
Opening routine
What is the area of a circle with radius of 3 m?
radius = r = 3
Area = π × r2 = π × 32
= π × (3 × 3)
= 3.14159... × 9
= 28.27 m2
Topic VII:
Properties of Circles
Topic VII Properties of Circles
Objective: Derive using similarity the fact that
the length of the arc intercepted by an angle
is proportional to the radius, and define the
radian measure of the angle as the constant
of proportionality.
Essential Question: How do you find the
length of an arc?
Topic VII Properties of Circles
Vocabulary
Circle - Is the set of all points in a plane equidistant
from a given point called the center of the circle.
Radius: Any segment with endpoints that are the center
of the circle and a point on the circle.
Chord: Segments with endpoints that are on the circle.
Diameter: A chord that passes by the center of the
circle.
Arc: Is a part of the circle that is defined by two
endpoints.
Topic VII Properties of Circles
Vocabulary
Minor arc: Is the shorter arc connecting two endpoints.
Major arc: Is the longest arc connecting two endpoints.
Semicircle: Is an arc that measures 180o
Central angle: An angle that intersects the circle in two
points and has its vertex at the center of the circle.
Inscribed angle: Is an angle that has its vertex on the
circle and sides that contain chords of the circle.
Topic VII Properties of Circles
Vocabulary
Sector: A sector of a circle is a region bounded by two
radii and their intercepted arc.
Tangent: A line which touches a circle at just one point.
Point of tangency: The point of tangency is the point at
which a line (called tangent) touches the circle.
Circumscribed polygon: Is a polygon which sides are
tangents to the circle.
Topic VII Properties of Circles
Topic VII Properties of Circles
Topic VII Properties of Circles
Topic VII Properties of Circles
Topic VII Properties of Circles
Topic VII Properties of Circles
Topic VII Properties of Circles
Topic VII Properties of Circles
Topic VII Properties of Circles
Topic VII Properties of Circles
Topic VII Properties of Circles
Topic VII Properties of Circles
Topic VII Properties of Circles
Guided Practice – WE DO
Topic VII Properties of Circles
Independent Practice – YOU DO
Arc Length and Sector Area
Worksheet
Exercises 1 - 26
Topic VII Properties of Circles
Re-teach MAFS.912.G-SRT.2.5: Use congruence and similarity
criteria for triangles to solve problems and to prove
relationships in geometric figures.
Math Nation Section 7 Topic 1 Independent Practice
Topic VII Properties of Circles
Re-teach MAFS.912.G-CO.3.9: Prove theorems about lines
and angles; use theorems about lines and angles to solve
problems.
Math Nation Section 3 Topic 6 Independent Practice
Topic VII Properties of Circles
Re-teach MAFS.912.G-CO.3.10: Prove theorems about
triangles; use theorems about triangles to solve problems.
Theorems include: measures of interior angles of a triangle
sum to 180°; base angles of isosceles triangles are congruent;
the segment joining midpoints of two sides of a triangle is
parallel to the third side and half the length; the medians of
a triangle meet at a point.
Math Nation Section 8 Topic 4 Independent Practice
Topic VII Properties of Circles
Closure
Essential Question How do you find the
length of an arc?
Topic VII Properties of Circles
Homework
Dilations Worksheet
Due Monday February 6, 2017