# Q4, W5: April 18-22 Geometry Teacher Kristin Andreason Geometry Honors 8 April 18-22 Unit 8: Circles with and without Coordinates
Standard(s) Taught

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 angles, circumscribed angles, diameters, radii, chords, tangents and
• 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.
Classroom Activities

Monday/Tuesday

1. Students will take notes on Inscribed Angles in their ISN
2. Students will do IXL U.11
3. Students will then finish previously assigned IXL’s or worksheets

Wednesday:

1. I will give students handouts on Tangents and Secants and we will go over them
2. Students will do IXL: New!  Angles formed by chords, secants, and tangents

Thursday/Friday:

1. Students will do an activity called “Build Understanding for the Equation of a Circle.”
2. We will watch some of Math Nation:  Section 12, Topic 5
3. I will introduce converting from the general form to the standard form of the equation of a circle by completing the square
4. Students will do a worksheet on Equations of Circles
Assignments Due
• IXL’s U.11 and New! Angles formed by chords, secants, and tangents
• Worksheet on Equations of Circles