*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.

**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 :**

Items may require the student to use slope or to find the distance

between points.Items may require the student to prove properties of triangles,

properties of quadrilaterals, properties of circles, and properties of

regular polygons.Items may require the student to use coordinate geometry to provide

steps to a proof of a geometric theorem.**Calculator :**Neutral

**Clarification :**

Students will use coordinate geometry to prove simple geometric

theorems algebraically**Stimulus Attributes :**

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

Items may require the student to determine if the algebraic proof is

correct.

**Test Item #:**Sample Item 1**Question:**One diagonal of square EFGH is shown on the coordinate grid.

There are two highlights in the sentence to show which word or phrase may be incorrect. For each highlight, click the word of phrase that is correct.

**Difficulty:**N/A**Type:**ETC: Editing Task Choice

## Related Courses

## Related Access Points

## Related Resources

## Formative Assessments

## Lesson Plans

## Problem-Solving Tasks

## MFAS Formative Assessments

Students are given the coordinates of the vertices of a quadrilateral and are asked to determine whether the quadrilateral could also be a parallelogram, rhombus, rectangle, square, or trapezoid.

Students are given the coordinates of three of the four vertices of a rectangle and are asked to determine the coordinates of the fourth vertex and show the diagonals of the rectangle are congruent.

Students are asked to prove that the quadrilateral formed by connecting the midpoints of the sides of a given quadrilateral is a parallelogram.

Students are given the coordinates of three vertices of a triangle and are asked to use algebra to determine whether the triangle is scalene, isosceles, or equilateral.

## 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

## 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