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Common Core: Math
CCLS - Math: G.C.3
- 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.
- 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 circle-secant or circle-secant-tangent 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...