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OBJECTIVE - G.C.A.3

Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle

INTERPRETATION OF OBJECTIVE - G.C.A.3

This objective is about constructing the circumcenter/circumcircle and the incenter/incircle of a triangle. This objective also has us establish the supplementary relationships between opposite angles of inscribed quadrilaterals.

SKILLS

(1) The student will be able to construct the circumcenter and circumcircle of a triangle.

(2) The student will be able to construct the incenter and the incircle of a triangle.

(3) The student will be able to prove that opposite angles of an inscribed quadrilateral in a circle are supplementary.

THE BIG IDEA

Circle constructions provide a way to connect circle properties to the physical construction. One of the themes of the entire curriculum in the inclusion of constructions as a way to visual and connect concepts.

TRAPS & PITFALLS

Students struggle to relate the construction to the actual experience... why did three perpendicular bisectors create a point that is the center of a circumscribed circle through each vertex? What is the difference between an incenter and a centroid or circumcenter? This tends to be technical and fairly unrelated and so it is difficult for students.

PAST CONNECTIONS

Throughout the entire year constructions are used to connect concepts in a visual way. Constructions are a physical way to demonstrating understanding.

FUTURE CONNECTIONS

Building confidence with constructions provide ways for students to work out future problems. The construction tools of straightedge and compass provide additional tools to solving geometry related problems.

MY REFLECTIONS (over line l)

I have always loved this unit.