They ensure the generality of their results by changing the dimensions and number of faces of the base. ![]() Students find the surface area of a regular pyramid (a pyramid with a regular polygon base) using a net that appears along a three-dimensional view of the pyramid. Based on their observations, students write formulas for area of a parallelogram and area of a triangle. Students discover that shearing does not affect the area, but changing the lengths of the height and base does. Students explore the relationship between the areas of parallelograms and triangles using a process called shearing. Parallel Pairs: Parallelogram and Triangle Area They construct a chord and its perpendicular bisector and discover a relationship between the chord’s length and its distance to the center of the circle, and they investigate and write a conjecture about congruent chords in a circle. Students explore the properties of chords in a circle. 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. zip activity files, right-click the download link and choose Save Target As to save to your computer. NOTE: If you are using Internet Explorer and are unable to download the.
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