Download Topic VII Properties of Circles Topic VII Properties of Circles Topic VII

Topic VII Properties of Circles
Opening routine
Circle A has the center at the origin
and a point D located on the circle
at (1, 0). Circle B has a center at
(1, 2) and the point E located on the
circle at (4, 2).
Logan performed two transformations
on circle A to show that circle A is
similar to circle B. He first dilates the
circle with the center of dilation at
the origin, and then translates the
new circle.
What are the algebraic descriptions
of the two transformations?
Topic VII Properties of Circles
Opening routine
The general rule for dilation by scale factor k
with center of dilation at (a, b) is:
Dk (x, y) = (a + k(x  a), b + k(y  b))
When the center of dilation is the origin,
a = 0 and b = 0, so the rule simplifies to:
Dk (x, y) = (kx, ky)
As the radius of the circle increases from
1 to 3, the scale factor is 3, then the
function for the dilation is:
D3 (x, y) = (3x, 3y).
The second transformation is a translation.
The function for translations is:
T(x, y) = (x + a, y + b)
This translation slides point D’ in (3, 0) to
point E in (4, -2), 1 unit to the right and 2
units down. Then the function for
translation is:
T(x, y) = (x + 1, y  2)
Topic VII Properties of Circles
Topic VII Properties of Circles
Topic VII:
Properties of Circles
Topic VII Properties of Circles
Objective: Identify and describe relationships
among inscribed angles, radii, and chords.
Include the relationship between central,
inscribed, and circumscribed angles.
Essential Question: How can you determine
the measures of central and inscribed angles
of a circle?
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
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
Properties of Circles
Guided Practice – WE DO
Topic VII Properties of Circles
Topic VII Properties of Circles
Topic VII Properties of Circles
Guided Practice – WE DO
If a square with sides
of 14 cm is inscribed
in a circle, what is the
diameter of the circle?
Topic VII Properties of Circles
Guided Practice – WE DO
As the triangle form
by the diagonal and two
of the sides of the square
is a 45o - 45o - 90o, the
length of the diagonal
is 2 times the length of
any of the sides.
d = 14 2
Topic VII Properties of Circles
Independent Practice – YOU DO
Central and Inscribed Angles
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 can you
determine the measures of central and
inscribed angles of a circle?
Topic VII Properties of Circles
Homework
Dilations Worksheet
Due Monday February 6, 2017