MAFS.912.G-C.1.2: Identify and describe relationships among inscribed angles, radii, and chords. (Include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle.)
MAFS.912.G-GPE.1.1: Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation.
|Learning Targets and Learning Criteria|
- identify central angles, inscribed and circumscribed angles, diameters, radii, chords, tangents
- use the sum of the measures of the central angels of a circle with no interior points in common is 360°.
- describe the relationship between a central angle, inscribed angle, or circumscribed angle and the arc it intercepts.
- recognize that an inscribed angle whose sides intersect the endpoints of the diameter of a circle is a right angle and that the radius of a circle is perpendicular to the tangent where the radius intersects the circle.
- use Pythagorean Theorem to prove lines tangent to a circle at its radius.
- identify the center and radius of a circle given its equation.
- draw a right triangle with a horizontal leg, a vertical leg, and the radius of a circle as its hypotenuse
- write the equation of a circle by using the distance formula (Pythagorean Theorem), the coordinates of a circle’s center, and the circle’s radius.
- rewrite an equation of a circle in general (quadratic) form to standard form by completing the square.
- Students will do an activity called “Build Understanding for the Equation of a Circle.”
- We will watch some of Math Nation Section 12, Topic 5
- Students will do IXL V.3
- I will give students notes on Tangents and Secants of Circles
- Student will do IXL: New! Angles formed by chords, secants, and tangents
- I will introduce completing the square
- I will show them how to convert from the general form to the standard form of the equation of a circle by completing the square
- We will do some of IXL V.5 together and then they will do for a grade
- IXL New! Angles formed by chords, secants, and tangents
- IXL V.5
All IEP and ESOL accommodations will be provided daily.