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A Midpoint Miracle

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A Midpoint Miracle

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.

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Connecting Givens to Proofs

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Connecting Givens to Proofs

Students will be able to identify givens that are necessary for completing a given quadrilateral proof.

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Finding Triangle Coordinates

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Finding Triangle Coordinates

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).

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Is this a Rectangle?

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Is this a Rectangle?

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.

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MARS Task: Classifying Equations of Parallel and Perpendicular Lines

Geometry
Unit 6: Coordinate Geometry
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MARS Task: Classifying Equations of Parallel and Perpendicular Lines

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.

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MARS Task: Square

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MARS Task: Square

In this task, you are given four points on a graph, and must prove that they are the corners of a square.

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Parallel Lines in the Coordinate Plane

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Parallel Lines in the Coordinate Plane

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.

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Perpendicular/Parallel Discovery

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Perpendicular/Parallel Discovery

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.

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Scaling a Triangle in the Coordinate Plane

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Scaling a Triangle in the Coordinate Plane

The goal of this task is to apply dilations to a triangle in the coordinate plane. 

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Side Splitter Theorem

Geometry
Unit 3: Similarity and Proof
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Side Splitter Theorem

Activity for students to explore how a segment inside a triangle and parallel to one side partitions the other 2 sides proportionally.

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