# Standard 2 : Use coordinates to prove simple geometric theorems algebraically. (Geometry - Major Cluster) (Archived)

This document was generated on CPALMS - www.cpalms.org

Clusters should not be sorted from Major to Supporting and then taught in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.

### General Information

Number: MAFS.912.G-GPE.2
Title: Use coordinates to prove simple geometric theorems algebraically. (Geometry - Major Cluster)
Type: Cluster
Subject: Mathematics - Archived
Domain-Subdomain: Geometry: Expressing Geometric Properties with Equations

#### Related Standards

This cluster includes the following benchmarks
Code Description
MAFS.912.G-GPE.2.4: Use coordinates to prove simple geometric theorems algebraically. For example, prove or disprove that a figure defined by four given points in the coordinate plane is a rectangle; prove or disprove that the point (1, √3) lies on the circle centered at the origin and containing the point (0, 2).

 Clarifications:Geometry - Fluency Recommendations Fluency with the use of coordinates to establish geometric results, calculate length and angle, and use geometric representations as a modeling tool are some of the most valuable tools in mathematics and related fields.
MAFS.912.G-GPE.2.5: Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point).

 Clarifications:Geometry - Fluency Recommendations Fluency with the use of coordinates to establish geometric results, calculate length and angle, and use geometric representations as a modeling tool are some of the most valuable tools in mathematics and related fields.
MAFS.912.G-GPE.2.6: Find the point on a directed line segment between two given points that partitions the segment in a given ratio.
MAFS.912.G-GPE.2.7: Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.
 Clarifications:Geometry - Fluency Recommendations Fluency with the use of coordinates to establish geometric results, calculate length and angle, and use geometric representations as a modeling tool are some of the most valuable tools in mathematics and related fields.

#### Related Access Points

This cluster includes the following access points.

#### Access Points

 Access Point Number Access Point Title MAFS.912.G-GPE.2.AP.4a: Use coordinates to prove simple geometric theorems algebraically. MAFS.912.G-GPE.2.AP.5a: Using slope, prove lines are parallel or perpendicular. MAFS.912.G-GPE.2.AP.5b: Find equations of lines based on certain slope criteria such as; finding the equation of a line parallel or perpendicular to a given line that passes through a given point. MAFS.912.G-GPE.2.AP.6a: Given two points, find the point on the line segment between the two points that divides the segment into a given ratio. MAFS.912.G-GPE.2.AP.7a: Use the distance formula to calculate perimeter and area of polygons plotted on a coordinate plane.

#### Related Resources

Vetted resources educators can use to teach the concepts and skills in this topic.

#### Original Student Tutorial

 Name Description High Tech Seesaw: Learn how to find the point on a directed line segment that partitions it into a given ratio in this interactive tutorial.

#### Perspectives Video: Professional/Enthusiasts

 Name Description Amping Up Violin Tuning with Math: Kyle Dunn, a Tallahassee-based luthier and owner of Stringfest, discusses how math is related to music.  Download the CPALMS Perspectives video student note taking guide. Cataloging Cats with Cartesian Coordinates: This researcher knows where your cat lives! Watch how he uses coordinates and the distance formula to plot the location of hundreds of thousands of cats on a map.

 Name Description A Midpoint Miracle: This problem solving task gives students the opportunity to prove a 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. Unit Squares and Triangles: This problem solving task asks students to find the area of a triangle by using unit squares and line segments. Triangles inscribed in a circle: This problem solving task challenges students to use ideas about linear functions in order to determine when certain angles are right angles.

#### Tutorials

 Name Description Parallel Lines: Parallel lines have the same slope and no points in common. However, it is not always obvious whether two equations describe parallel lines or the same line. Perpendicular Lines: Perpendicular lines have slopes which are negative reciprocals of each other, but why?

#### Video/Audio/Animations

 Name Description Parallel Lines 2: This video shows how to determine which lines are parallel from a set of three different equations. Parallel Lines: This video illustrates how to determine if the graphs of a given set of equations are parallel. Perpendicular Lines 2: This video describes how to determine the equation of a line that is perpendicular to another line. All that is given initially the equation of a line and an ordered pair from the other line.

#### Worksheet

 Name Description Midpoints of the Sides of a Quadrilateral: The students will construct a quadrilateral on graph paper, determine the midpoints of each of the four sides, then connect the midpoints of adjacent sides. The question then is the following: what are the properties of the resulting quadrilateral? Students need to justify their conclusions.

#### Student Resources

Vetted resources students can use to learn the concepts and skills in this topic.

#### Original Student Tutorial

 Title Description High Tech Seesaw: Learn how to find the point on a directed line segment that partitions it into a given ratio in this interactive tutorial.

 Title Description A Midpoint Miracle: This problem solving task gives students the opportunity to prove a 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. Unit Squares and Triangles: This problem solving task asks students to find the area of a triangle by using unit squares and line segments. Triangles inscribed in a circle: This problem solving task challenges students to use ideas about linear functions in order to determine when certain angles are right angles.

#### Tutorials

 Title Description Parallel Lines: Parallel lines have the same slope and no points in common. However, it is not always obvious whether two equations describe parallel lines or the same line. Perpendicular Lines: Perpendicular lines have slopes which are negative reciprocals of each other, but why?

#### Video/Audio/Animations

 Title Description Parallel Lines 2: This video shows how to determine which lines are parallel from a set of three different equations. Parallel Lines: This video illustrates how to determine if the graphs of a given set of equations are parallel. Perpendicular Lines 2: This video describes how to determine the equation of a line that is perpendicular to another line. All that is given initially the equation of a line and an ordered pair from the other line.

#### Parent Resources

Vetted resources caregivers can use to help students learn the concepts and skills in this topic.