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

TeacherKristin Andreason
Subject AreaGeometry Honors
Grade Level8
Week #April 15-19
Unit of InstructionUnit 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.
Additional Resources

All IEP and ESOL accommodations will be provided daily.