Big Idea:

Big Idea 3

Congruence and similarity criteria prove relationships between segments and figures of a circle.

1 week

Evidence of Understanding

  • investigate and describe the relationships that exist between the segments on a circle
    • investigate and describe how the lengths of segments for two intersecting chords, two secants (drawn from the same point), or a tangent and a secant (drawn from the same point) are related
      • prove theorems about the segments of secants, tangents, or intersecting chords
    • recognize congruent chords are equidistant from the center of the circle
    • recognize tangents from a shared point outside the circle are congruent
    • calculate the length of an unknown segment
       
  • analyze and apply characteristics of polygons that circumscribe or are inscribed in a circle
    • use constructions to visualize the congruent relationships when inscribing or circumscribing a polygon in the circle
      • construct an equilateral triangle, square or regular hexagon inscribed in a circle
      • construct a right triangle inscribed in a circle using perpendicular bisectors
      • construct a circle that is inscribed in a triangle using angle bisectors
    • use constructions to identify and define the incenter of a triangle
    • prove properties of angles for a quadrilateral inscribed in a circle
      • Example: quadrilaterals inscribed in a circle have opposite angles that are supplementary
    • find the missing value of an unknown angle or segment involving a polygon and a circle
       
  • use circles in modeling situations and find missing values
    • create diagrams that can be used to represent the situation
    • use markings and notations to create equations that can be used to find missing values

Develop conceptual understanding:

chord, secant, tangent, secants, inscribed, circumscribed, incenter 

Supporting terms to communicate:

radius, equivalent, ratio, proportion, similarity, scale factor, dilation, right triangle, equilateral, regular polygon, quadrilateral, perpendicular,  bisect, intersect, intercepted arc, supplementary

Search for resources related to this big idea by following this link.

Core Resource
A core resource supports multiple days of instruction.
  • Circles and Segments
    These four parts are designed to support students in making connections between chord, secant, and tangent line relationships in circles and creating proofs of these relationships using triangle similarity.
    Resource:
    Circles and Segments

    These four parts are designed to support students in making connections between chord, secant, and tangent line relationships in circles and creating proofs of these relationships using triangle similarity.

    All Resources From:
Instructional Routine: Contemplate then Calculate
These tasks are embedded within the instructional routine called Contemplate then Calculate. COMING SOON!
    Instructional Routine: Connecting Representations
    These tasks are embedded within the instructional routine called Connecting Representations.