### Remarks

**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.

**Subject Area:**Mathematics

**Grade:**912

**Domain-Subdomain:**Geometry: Expressing Geometric Properties with Equations

**Cluster:**Level 2: Basic Application of Skills & Concepts

**Cluster:**Use coordinates to prove simple geometric theorems algebraically. (Geometry - Major Cluster) -

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.

**Date Adopted or Revised:**02/14

**Date of Last Rating:**02/14

**Status:**State Board Approved - Archived

**Assessed:**Yes

**Assessment Limits :**

Lines may include horizontal and vertical lines.Items may not ask the student to provide only the slope of a parallel

or perpendicular line.**Calculator :**Neutral

**Clarification :**

Students will prove the slope criteria for parallel lines.Students will prove the slope criteria for perpendicular lines.

Students will find equations of lines using the slope criteria for

parallel and perpendicular lines.**Stimulus Attributes :**

Items may be set in a real-world or mathematical context.**Response Attributes :**

Items may require the student to be familiar with slope-intercept

form of a line, standard form of a line, and point-slope form of a line.

**Test Item #:**Sample Item 1**Question:**The equation for line A is shown.

y=

Line A and line B are perpendicular, and the point (-2,1_ lies on line B.

Write an equation for line B.

**Difficulty:**N/A**Type:**EE: Equation Editor

## Related Courses

## Related Access Points

## Related Resources

## Formative Assessments

## Lesson Plans

## Problem-Solving Tasks

## Tutorials

## Video/Audio/Animations

## Worksheet

## MFAS Formative Assessments

Students are asked to prove that two parallel lines have equal slopes.

Students are asked to prove that two lines with equal slopes are parallel.

Students are asked to prove that the slopes of two perpendicular lines are both opposite and reciprocal.

Students are asked to prove that if the slopes of two lines are both opposite and reciprocal, then the lines are perpendicular.

Students are asked to identify the slope of a line parallel to a given line and write an equation for the line given a point.

Students are asked to identify the slope of a line perpendicular to a given line and write an equation for the line given a point.

## Student Resources

## Problem-Solving Tasks

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.

Type: Problem-Solving Task

This problem solving task asks students to find the area of a triangle by using unit squares and line segments.

Type: Problem-Solving Task

This problem solving task challenges students to use ideas about linear functions in order to determine when certain angles are right angles.

Type: Problem-Solving Task

## Tutorials

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.

Type: Tutorial

Perpendicular lines have slopes which are negative reciprocals of each other, but why?

Type: Tutorial

## Video/Audio/Animations

This video shows how to determine which lines are parallel from a set of three different equations.

Type: Video/Audio/Animation

This video illustrates how to determine if the graphs of a given set of equations are parallel.

Type: Video/Audio/Animation

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.

Type: Video/Audio/Animation

## Parent Resources

## Problem-Solving Tasks

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.

Type: Problem-Solving Task

This problem solving task asks students to find the area of a triangle by using unit squares and line segments.

Type: Problem-Solving Task

This problem solving task challenges students to use ideas about linear functions in order to determine when certain angles are right angles.

Type: Problem-Solving Task