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This classroom task gives students the opportunity to prove a surprising fact about quadrilaterals: that if we join the midpoints of an arbitrary quadrilateral to form a new quadrilateral, then the new quadrilateral is a parallelogram, even if the original quadrilateral was not.

School mapped out on a grid that applies length and slope.

The purpose of this task is to use similar triangles in order to study the coordinates of points which divide a line segment in a given ratio. These coordinates can be calculated directly but the method employed here not only allows us to find the coordinates of the desired points but also to construct them (with straightedge and compass).

Real world application of coordinate geometry.

The goal of this task is to provide an opportunity for students to apply a wide range of ideas from geometry and algebra in order to show that a given quadrilateral is a rectangle. Creativity will be essential here as the only given information is the Cartesian coordinates of the quadrilateral's vertices.

This lesson unit is intended to help you assess how well students understand the relationship between the slopes of parallel and perpendicular lines and in particular, to help identify students who find it difficult to:
Find, from their equations, lines that are parallel and perpendicular.
Identify and use intercepts.
It also aims to encourage discussion on some common misconceptions about equations of lines.

The goal of this task is to prove the slope criterion for parallel lines. There are several subtleties to address, including:
separating out the case of vertical lines which do not have well-defined slope,
establishing both implications (parallel lines have equal slope and lines of equal slope are parallel),
relating the algebra of the linear equations to the geometry of lines.

This discovery lesson has students determine slopes of a series of lines and then pairing them as parallel, perpendicular or neither.  Once they are paired, students have to determine how they know that lines are perpendicular.

This folder has a cover pages and six extended, scaffolded problems that are designed for an end-of-year trip to Six Flags Great America. It covers linear and quadratic functions and transformations. The problems refer specifically to the rides and experiences that students will have while at the park, while at the same time most of the problems can be finished at home or on the bus. Each problem has a rubric for standard-based scoring of problems. Feel free to download and change at will. Please don't change the originals.

The goal of this task is to use similar triangles to establish the slope criterion for perpendicular lines. Students need to be familiar with scaling and with the side-side-side congruence criterion.

The goal of this task is to examine when two lines in the plane are perpendicular in terms of their slopes.