# Q4, W4: Geometry Honors (April 15-19)

Teacher Kristin Andreason Geometry Honors 8 April 15-19 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-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).
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Classroom Activities

Monday/Tuesday:

• 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.

Wednesday:

• Students will finish their representations and we will finish the presentations.

Thursday:

• 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.
Assignments Due
• Visual representations are due by Wednesday, April 17.