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-C.1.3: Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle.
|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.
- apply the Arc Addition Postulate to solve for missing arc measures.
- prove that opposite angles in an inscribed quadrilateral are supplementary.
- define the terms inscribed, circumscribed, angle bisector, and perpendicular bisector.
- construct the inscribed circle whose center is the point of intersection of the angle bisectors (the incenter).
- construct the circumscribed circle whose center is the point of intersection of the perpendicular bisectors of each side o the triangle (the circumcenter).
- Students will do a circle theorem discovery activity by measuring angles in circles.
- Students will then use the Geogebra applet to manipulate angles within a circle to see that the theorems are true for all angles.
- Students will create a visual representation of one of the circle theorems.
- Students will then present their theorem to the class and show how they used it to solve their particular problems.
- Students will finish their representations and we will finish the presentations.
- Students will learn how to inscribe a circle in a triangle and how to construct the circumscribed circle of a triangle using compasses.
- We will use Math Open Reference as a demonstration and then will practice to understand what is needed to inscribe and circumscribe a circle.
- Visual representations are due by Wednesday, April 17.
All IEP and ESOL accommodations will be provided daily.