Coordinate Geometry

8 Components
Initial Task
Squares and Rectangles
Big Ideas
Big Idea 1 Big Idea 2
Formative Assessment Lesson
Finding Equations of Parallel and Perpendicular Lines
Re-engagement
Re-engagement for Unit 6
End of Unit Assessments
End of Unit Assessment for Unit 6 End of Unit Assessment Teacher Resources for GEO Unit 6 Find aligned Regents questions with Quiz Banker
Geo U6: Coordinate Geometry
Unit Outline
Initial Task
Squares and Rectangles
Big Ideas
Big Idea 1 Big Idea 2
Formative Assessment Lesson
Finding Equations of Parallel and Perpendicular Lines
Re-engagement
Re-engagement for Unit 6
End of Unit Assessments
End of Unit Assessment for Unit 6 End of Unit Assessment Teacher Resources for GEO Unit 6 Find aligned Regents questions with Quiz Banker
None
Geo U6:

Coordinate Geometry

How are coordinates used to prove geometric relationships?
3 weeks
See Standards
Common Core: Major Standards:
G-CO.B.6

Understand congruence in terms of rigid motions. Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent.

G-CO.C.10

Prove geometric theorems. Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180°; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point. Clarification: Theorems include but are not limited to the listed theorems. Example: an exterior angle of a triangle is equal to the sum of the two non-adjacent interior angles of the triangle

G-CO.C.11

Prove geoemtric theorems. Prove theorems about parallelograms. Theorems include: opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and conversely, rectangles are parallelograms with congruent diagonals.

G-SRT.A.1

Understand similarity in terms of similarity transformations. Verify experimentally the properties of dilations given by a center and a scale factor: A dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged. The dilation of a line segment is longer or shorter in the ratio given by the scale factor.

G-SRT.A.2

Understand similarity in terms of similarity transformations. Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.

G-GPE.B.4

Use coordinates to prove simple geometric theorems algebraically. 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).

G-GPE.B.5

Use coordinates to prove simple geometric theorems algebraically. 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).

G-GPE.B.6

Use coordinates to prove simple geometric theorems algebraically. Find the point on a directed line segment between two given points that partitions the segment in a given ratio.

G-GPE.B.7

Use coordinates to prove simple geometric theorems algebraically. Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula. 

Unit six is about using the coordinate plane to prove the similarity and congruence relationships from previous units analytically. Students use coordinates to verify geometric relationships by finding slope and distance of a line to support their proof. This unit provides students with the opportunity to refine their understanding of basic geometric theorems and transformations.

Essential Questions:

  • How are coordinates used to prove relationships between lines/segments and within segments?
  • How are coordinates used to prove relationships and find measurements of polygons?
Printable Unit Plan
  • Geometry Unit Plan for Unit 6
    Resource:
    Geometry Unit Plan for Unit 6

    This is a printable version of the entire unit plan. You can make a copy of it and edit it or download and print it as needed.

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Unit Outline

8 Components

Every unit begins with an Initial Task and ends with a Balanced Assessment, both focusing on core mathematics of the unit. The core mathematics is developed through a series of resources around Big Ideas; as you move through the unit, keep students focused on how these ideas are connected and how they address mathematical problem solving. Before attempting the Balanced Assessment, students have an opportunity to synthesize their knowledge through a multi-day Formative Assessment Lesson and teacher-designed re-engagement lessons.

Initial Task See 1 itemHide 1 item

Big Ideas See 2 itemsHide 2 items

Formative Assessment Lesson See 1 itemHide 1 item

Re-engagement See 1 itemHide 1 item

End of Unit Assessments See 3 itemsHide 3 items