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
Browse 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
Big Idea:

Big Idea 2

A polygon is categorized by the length and direction of its line segments on the coordinate plane.

1 week
See Standards
Common Core: Major Standards:
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. 

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.

Evidence of Understanding

  • analyze and describe characteristics of polygons on the coordinate plane
    • calculate the length and direction of sides of a polygon using the slope and distance formulas
    • determine the length or direction of a line segment in relation to the sides of a polygon (including an altitude, perpendicular bisector, etc.)
    • compare polygons using the length or direction of their sides, angle, or diagonals to describe how they are similar, congruent, or neither
    • calculate and compare the perimeter of various polygons on the coordinate plane
      • use the distance formula, Pythagorean Theorem, etc.
    • calculate areas of triangles or rectangles on the coordinate plane
      • identify points that are needed to calculate area of triangles and rectangles
      • explore when area changes or stays the same based on the lengths being used (Example: height of a triangle)
    • transform polygons and describe the relationship between a pre-image and its image under a transformation on the coordinate plane
      • apply and justify the ratio of the scale factor on perimeter and area
  • prove geometric relationships on the coordinate plane
    • prove two figures are congruent or similar in the coordinate plane
      • use similarity relationships to determine ratios between segments
    • classify a polygon using characteristics of its sides, angles, and diagonals
      • determine what information is sufficient to prove the classification of a triangle/ quadrilateral
      • given a specified polygon, find coordinates of points or lengths or directions of line segments that make the classification valid

Develop conceptual understanding:

perimeter, area

Supporting terms to communicate:

slope, distance, length, parallel, perpendicular, partition, dilation, equilateral, right, isosceles, quadrilateral, rectangle, square, rhombus, parallelogram, diagonals, bisect, midpoint, perpendicular bisector, height, base

Core Resource

A core resource supports multiple days of instruction.

  • Proving Polygons
    This Core Resource is where students use tools related to the coordinate plane to classify polygons and prove polygons congruent or similar to each other.
    Resource:
    Proving Polygons

    Geometry & Algebra II Archive

    Geo U6: Coordinate Geometry

    Big Idea: Big Idea 2

    This Core Resource is where students use tools related to the coordinate plane to classify polygons and prove polygons congruent or similar to each other.

    Preview ResourceAdd a Copy of Resource to my Google Drive
    Type
    Geometry: Coordinate Geometry
    File
    Google Doc
    Tags
    coordinate plane, polygons
    Standards
    Common Core: Major Standards ( G-CO.B.6, G-CO.C.10, G-CO.C.11, G-SRT.A.1, G-SRT…
    +— Details
    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. 

    All Resources From:
Instructional Routine: Contemplate then Calculate
These tasks are embedded within the instructional routine called Contemplate then Calculate.
Instructional Routine: Sharing Skepticism

The primary goal of this instructional routine is to support students in constructing and critiquing mathematical arguments.