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Common Core: Math
CCLS  Math: G.C.3
 Category
 Circles
 SubCategory
 Understand And Apply Theorems About Circles
 State Standard:
 Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle.
9 Results

 Student Outcomes Students determine the area of a cyclic quadrilateral as a function of its side lengths and the acute angle formed by its diagonals. Students prove Ptolemy’s theorem, which states...

 Student Outcomes Students show that a quadrilateral is cyclic if and only if its opposite angles are supplementary. Students derive and apply the area of cyclic quadrilateral ABCD as 1/2 AB·CD·sin(w...

 The module concludes with Topic E focusing on the properties of quadrilaterals inscribed in circles and establishing Ptolemy's theorem. This result codifies the Pythagorean theorem, curious facts...

 Student Outcomes Students find “missing lengths” in circlesecant or circlesecanttangent diagrams.

 In Topic C, students explore geometric relations in diagrams of two secant lines, or a secant and tangent line (possibly even two tangent lines), meeting a point inside or outside of a circle. They...

 Student Outcomes Inscribe a rectangle in a circle. Understand the symmetries of inscribed rectangles across a diameter.

 Student Outcomes Using observations from a pushing puzzle, explore the converse of Thales' theorem: If triangle ABC is a right triangle, then A, B, and C are three distinct points on a circle with...

 Topic A leads students first to Thales' theorem (an angle drawn from a diameter of a circle to a point on the circle is sure to be a right angle), then to possible converses of Thales' theorem, and...

 Geometry Module 5: Circles With and Without Coordinates This module brings together the ideas of similarity and congruence and the properties of length, area, and geometric constructions studied...