This task challenges a student to use geometric properties of circles and triangles to prove that two
triangles are congruent. A student must be able to use congruency and corresponding parts to reason
about lengths of sides. A student must be able to construct lines to make sense of a diagram. A
student needs to use geometric properties to find the radius of a circle inscribed in a right triangle.
Students construct a parallelogram, measure the side lengths and angles, and observe that opposite sides are congruent, opposite angles are congruent, and consecutive angles are supplementary. Then they construct the diagonals, measure the distances from the vertices to the point of intersection, and discover that the diagonals bisect each other.
This lesson unit is intended to help you assess how well students are able to produce and evaluate geometrical proofs. In particular, this unit is intended to help you identify and assist students who have difficulties in:
Identifying mathematical knowledge relevant to an argument.
Linking visual and algebraic representations.
Producing and evaluating mathematical arguments.
This lesson unit is intended to help you assess how well students can:
Understand the concepts of length and area.
Use the concept of area in proving why two areas are or are not equal.
Construct their own examples and counterexamples to help justify or refute conjectures.
This task challenges a student to use geometric properties to find and prove relationships about an inscribed
quadrilateral. A student must analyze characteristics and properties of 2?dimensional figures and develop
mathematical arguments of the relationships within the figures.