They dilate the polygon to approximately a single point to create a visual proof by dilation that the sum of the measures of the exterior angles of a convex polygon is what they conjectured. Students construct a convex polygon and make a conjecture about the sum of the measures of its exterior angles. They discover that the midpoint quadrilateral is a parallelogram and prove this conjecture. Students connect the midpoints of a quadrilateral to construct a midpoint quadrilateral. Then they construct the diagonals, measure the distances from the vertices to the point of intersection, and discover that the diagonals bisect each other. Students construct a parallelogram, measure side lengths and angles, and observe that opposite sides are congruent, opposite angles are congruent, and consecutive angles are supplementary.
Meet the Parallelogram: Properties of Parallelograms As they make distinctions on the basis of characteristics, they deepen their understanding of the definitions of various quadrilaterals, their properties, and the relationships among them. Students drag edges and vertices of various Sketchpad quadrilaterals to discover which are constructed to have specific characteristics. Quadrilateral Pretenders: Classifying Quadrilaterals They observe the concurrence of the medians, measure distances to observe how the centroid divides each median, and make a custom tool for constructing the centroid of a given triangle. Students construct a triangle and its medians. View Overview | Download Activity Files (.zip)
Students construct an irregularly-shaped tile based on an equilateral triangle, and then use rotation to tessellate the plane with it.
#Geometers sketchpad activities zip#
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