G.GPE.4-7
2011
Domain Expressing Geometric Properties with Equations
Cluster Use coordinates to prove simple geometric theorems algebraically
Standards
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).
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).
6. Find the point on a directed line segment between two given points that partitions the segment in a given ratio.
7. Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.*
Essential Questions
Enduring Understandings
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How do you use
coordinate geometry to
prove theorems?
What properties of
geometric figures can
be proven using
coordinate geometry?
How can you derive the
distance and midpoint
formulas using
coordinate geometry?
How can you calculate
areas using coordinate
geometry?
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Students will understand the
relationship between algebra
and coordinate geometry.
Students will understand the
concept of slope and how it
relates to geometric figures.
Activities, Investigation, and Student Experiences
1. PowerPoint lessons, Interactive Examples, Worksheets
G.GPE.4-7
Content Statements
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Students will be able to
use coordinate
geometry to prove
geometric theorems
algebraically.
Students will be able to
use slope to prove lines
are parallel or
perpendicular.
Students will be able to
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.
Students will be able to
find a point on a line
segment that divides the
segment into a given
ratio when given two
points.
Students will be able to
use coordinate
geometry and the
distance formula to find
the perimeters of
polygons and the areas
of triangles and
2011
G.GPE.4-7
2011
rectangles.
Assessments
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Student Participation
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Questioning
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Quizzes (Teacher Given and Self Quizzes)
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Benchmark/Test
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Homework
Equipment Needed:
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SMARTboard
Projector
Paper and pencil
Calculator (Graphing and Scientific)
Compass
Protractor
Ruler
Straightedge
Graph Paper
Isometric Dot Paper
Hands-on and virtual two- and three-dimensional
manipulatives (i.e. prisms)
Geo-boards
Geometer’s Sketchpad
Teacher Resources:
1. Math Warehouse Website:
http://www.mathwarehouse.com/algebra/linear_equation/par
allel-perpendicular-lines.php
G.GPE.4-7
2011