**Name** |
**Description** |

Proof of Quadrilaterals in Coordinate Plane: | This lesson is designed to instruct students on how to identify special quadrilaterals in the coordinate plane using their knowledge of distance formula and the definitions and properties of parallelograms, rectangles, rhombuses, and squares. Task cards, with and without solution-encoded QR codes, are provided for cooperative group practice. The students will need to download a free "QR Code Reader" app onto their SmartPhones if you choose to use the cards with QR codes. |

Airplanes in Radar's Range: | For a given circle m and point A in a coordinate plane, students will be able to show whether this given point A lies on the circumference of the given circle m using the Pythagorean Theorem. Subsequently, this can be used to prove that an airplane lies within or outside the radar's range with a given radius of detection. |

Partition Point For The Queen: | Students will use a variety of methods to locate a point to partition a line segment to a given ratio. The activities will range from informal student definitions and sketches to tasks using number lines and the coordinate plane. |

Who Am I?: Quadrilaterals: | Students will use formulas they know (distance, midpoint, and slope) to classify quadrilaterals. |

Pondering Points Proves Puzzling Polygons: | In a 55 minute class, students use whiteboards, Think-Pair-Share questioning, listen to a quadrilateral song, and work individually and in groups to learn about and gain fluency in using the distance and slope formulas to prove specific polygon types. |

Geometree Thievery: | This geometry lesson focuses on partitioning a segment on a coordinate grid in a non-traditional and interesting format. Students will complete a series of problems to determine which farmers are telling the truth about their harvested "Geometrees." |

Proving quadrilaterals algebrically using slope and distance formula: | Working in groups, students will prove the shape of various quadrilaterals using slope, distance formula, and polygon properties. They will then justify their proofs to their classmates. |

Quadrilaterals and Coordinates: | In this lesson, students will use coordinates to algebraically prove that quadrilaterals are rectangles, parallelograms, and trapezoids. |

My Geometry Classroom: | Students will learn how to find the area and perimeter of multiple polygons in the coordinate plane using the composition and decomposition methods, with the support of previous knowledge on the Distance Formula and Pythagorean Theorem. Students will complete a *Geometry Classroom Floor Plan *group activity. Students will do a short presentation to discuss their results that leads to the realization that polygons with the same perimeter can have different areas. Students will also complete an independent practice and submit an exit ticket at the end of the lesson. |

Partitioning a Segment: | In this lesson, students find the point on a directed line segment between two given points that partitions the segment in a given ratio. |

Proving Quadrilaterals: | This lesson provides a series of assignments for students at the *Getting Started*, *Moving Forward*, and *Almost There* levels of understanding for the Mathematics Formative Assessment System (MFAS) Task Describe the Quadrilateral (CPALMS Resource ID#59180). The assignments are designed to "move" students from a lower level of understanding toward a complete understanding of writing a coordinate proof involving quadrilaterals. |

What's the Point?: | Students will algebraically find the missing coordinates to create a specified quadrilateral using theorems that represent them, and then algebraically prove their coordinates are correct.
Note: This is not an introductory lesson for this standard. |

Polygon...Prove it: | While this is an introductory lesson on the standard, students will enjoy it, as they play "Speed Geo-Dating" during the Independent practice portion. Students will use algebra and coordinates to prove rectangles, rhombus, and squares. Properties of diagonals are not used in this lesson. |

Partition Me: | Partition, what's that? Well come find out as you learn to break it down, a segment that is. Learn the basic skills of partitioning and you can turn your class into a partitioning party; just BYOGP (Bring your own graph paper). |

Just Plane Ol' Area!: | Students will construct various figures on coordinate planes and calculate the perimeter and area. Use of the Pythagorean theorem will be required. |

Going the Distance: | This lesson uses the Pythagorean Theorem to derive several iterations of the Distance Formula. The Distance Formula is then used to calculate the distance between two points on both directional maps and the Cartesian coordinate plane. Vocabulary relating to vectors is also introduced. |

Graphing Equations on the Cartesian Plane: Slope: | The lesson teaches students about an important characteristic of lines: their slope. Slope can be determined either in graphical or algebraic form. Slope can also be described as positive, negative, zero, or undefined. Students get an explanation of when and how these different types of slope occur. Finally, students learn how slope relates to parallel and perpendicular lines. When two lines are parallel, they have the same slope and when they are perpendicular their slopes are negative reciprocals of one another. Prerequisite knowledge: Students must know how to graph points on the Cartesian plane. They must be familiar with the x- and y- axes on the plane in both the positive and negative directions. |

"When will we ever meet?": | Students will be guided through the investigation of y = mx+b. Through this lesson, students will be able to determine whether lines are parallel, perpendicular, or neither by looking at the graph and the equation. |

Forget Waldo - Where is 'the orthocenter'?: | Starting with a set of three points, students will practice finding equations of lines and the lines that are perpendicular to them. The students will repeat this process three times - using different colors for differentiating one line from the next. The big finale brings all the work together and the students realize this activity leads to finding the orthocenter of a triangle. |

Investigating Lines With Our Minds!: | A discovery investigation for the slopes of parallel and perpendicular lines. Students write the equations of lines parallel and/or perpendicular to a given line through a given point. Directions for using graph paper or x-y coordinate pegboards are given. |