UNIT 4
GEOMETRY
TEMPLATE CREATED BY
REGION 1 ESA
UNIT 4
Geometry Math Tool Unit 4
Geometry Unit 4 Overview: Connecting Algebra and Geometry Through
Coordinates
Building on their work with the Pythagorean theorem in 8th grade to find distances, students use
a rectangular coordinate system to verify geometric relationships, including properties of special
triangles and quadrilaterals and slopes of parallel and perpendicular lines. Students continue their
study of quadratics by connecting the geometric and algebraic definitions of the parabola.
Template created by Region 1 ESA
Page 2 of 8
Geometry Math Tool Unit 4
Unit 4: Connecting Algebra and Geometry Through Coordinates G.GPE.4
Cluster: Use coordinates to prove simple geometric theorems algebraically.
Standard
Instructional Notes: This unit has a close connection with the
next unit. For example, a curriculum might merge G.GPE.1 and
the Unit 5 treatment of G.GPE.4 with the standards in this unit.
Reasoning with triangles in this unit is limited to right
triangles; e.g., derive the equation for a line through two
points using similar right triangles.
G.GPE.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).
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Content/Skills Included in Textbook
(Include page numbers and comments)
Suggested Learning Targets



I can represent the vertices of a figure in the
coordinate plane using variables.
I can connect a property of a figure to the
tool needed to verify that property.
I can use coordinates and the right tool to
prove or disprove a claim about a figure.
For example:
 Use slope to determine if sides are
parallel, intersecting, or perpendicular.;
 Use the distance formula to determine if
sides are congruent or to decide if a
point is inside a circle, outside a circle, or
on the circle;
 Use the midpoint formula or the
distance formula to decide if a side has
been bisected.
Essential Questions/ Enduring Understandings
 How can algebra be useful when expressing
geometric properties?
Algebra can be used to efficiently and
effectively describe and apply geometric
properties.
Assessment
Assessments align to suggested learning targets.
Directly
Aligned
Somewhat
Aligned
Not
Aligned
Check all assessment types that address this standard
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Drill and practice
Multiple choice
Short answer (written)
Performance (verbal explanation)
Product / Project
Vocabulary
Side length, vertex, first quadrant, slope, distance, midpoint, parallel, perpendicular, intersecting
Template created by Region 1 ESA
Page 3 of 8
Geometry Math Tool Unit 4
Unit 4: Connecting Algebra and Geometry Through Coordinates G.GPE.5
Cluster: Use coordinates to prove simple geometric theorems algebraically.
Standard
Suggested Learning Targets
Instructional Notes: This unit has a close connection with the
next unit. Relate work on parallel lines in G.GPE.5 to work on
A.REI.5 in High School Algebra I involving systems of equations
having no solution or infinitely many solutions.
Parallel Lines:
 I can draw a line on a coordinate plane and
translate that line to produce its image.
 I can explain that these lines are parallel
since translations preserve angle.
 I can determine slopes of the original line
and its image after translation and show
they have the same slope using specific
examples and general coordinates (x,y).
 I can state that parallel line have the same
slope.
 I can determine if lines are parallel using
their slop.
 I can write an equation for a line that is
parallel to a given line that passes through a
given point.
Essential Questions/ Enduring Understandings
 How can algebra be useful when expressing
geometric properties?
Algebra can be used to efficiently and
effectively describe and apply geometric
properties.
G.GPE.5 Prove the slope criteria for parallel and
perpendicular lines and uses 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).
Directly
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Aligned
Aligned
Aligned
Content/Skills Included in Textbook
(Include page numbers and comments)
Assessment
Assessments align to suggested learning targets.
Directly
Aligned
Somewhat
Aligned
Not
Aligned
Check all assessment types that address this standard





Drill and practice
Multiple choice
Short answer (written)
Performance (verbal explanation)
Product / Project
Vocabulary
Slope, parallel, coordinate plane, translations, coordinates (x, y)
Template created by Region 1 ESA
Page 4 of 8
Geometry Math Tool Unit 4
Unit 4: Connecting Algebra and Geometry Through Coordinates G.GPE.5 continued
Cluster: Use coordinates to prove simple geometric theorems algebraically.
Standard
Suggested Learning Targets
Instructional Notes: This unit has a close connection with the
next unit. Relate work on parallel lines in G.GPE.5 to work on
A.REI.5 in High School Algebra I involving systems of equations
having no solution or infinitely many solutions.
Perpendicular Lines:
 I can draw a line on a coordinate plane and
rotate that line 90⁰ to produce a
perpendicula image.
 I can determine the slope of the original line
and its image after a 90⁰ rotation and show
they have the opposite reciprocal slopes
using specific examples and genreal
coordiantes (x, y)
 I can state that perpendicular lines have the
opposite reciprocal slopes.
 I can determine if lines ar eperpendicular
using their slope.
 I can write an equation for a line that is
perpendicular to a given line that passes
through a given point.
Essential Questions/ Enduring Understandings
 How can algebra be useful when expressing
geometric properties?
Algebra can be used to efficiently and
effectively describe and apply geometric
properties.
G.GPE.5 Prove the slope criteria for parallel and
perpendicular lines and uses 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).
Directly
Somewhat
Not
Aligned
Aligned
Aligned
Content/Skills Included in Textbook
(Include page numbers and comments)
Assessment
Assessments align to suggested learning targets.
Directly
Aligned
Somewhat
Aligned
Not
Aligned
Check all assessment types that address this standard





Drill and practice
Multiple choice
Short answer (written)
Performance (verbal explanation)
Product / Project
Vocabulary
Slope, parallel, coordinate plane, translations, coordinates (x, y), product, line, linear equation,
slope-intercept form, point-slope form
Template created by Region 1 ESA
Page 5 of 8
Geometry Math Tool Unit 4
Unit 4: Connecting Algebra and Geometry Through Coordinates G.GPE.6
Cluster: Use coordinates to prove simple geometric theorems algebraically.
Standard
Instructional Notes: none
G.GPE.6 Find the point on a directed line segment between
two given points that partitions the segment in a given ratio.
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Content/Skills Included in Textbook
(Include page numbers and comments)
Suggested Learning Targets

I can calculate the point(s) on a directed line
segment whose endpoints are (𝑥1, 𝑦1 ) and
(𝑥2, 𝑦2 ) that partitions the line segment into
a given ratio, 𝑟1 to 𝑟2 using the formula
𝑟 𝑥
𝑟1 𝑥2
𝑟 𝑦
𝑟1 𝑦2
x = 2 1+
y = 2 1+
(e.g.,
𝑟 +𝑟
𝑟 +𝑟
1
2
1
2
for the directed line segment whose
endpoints are (0,0) and (4,3), the point that
partitions the segment into a ratio of 3 to 2
can be found
x=
(2∙0+3∙4) 12
=
(3+2)
5
(2∙0+3∙3) 9
=
(3+2)
5
and y=
so the
point is (12/5, 9/5). (R)
Essential Questions/ Enduring Understandings
 How can algebra be useful when expressing
geometric properties?
Algebra can be used to efficiently and
effectively describe and apply geometric
properties.
Assessment
Assessments align to suggested learning targets.
Directly
Aligned
Somewhat
Aligned
Not
Aligned
Check all assessment types that address this standard





Drill and practice
Multiple choice
Short answer (written)
Performance (verbal explanation)
Product / Project
Vocabulary
Directed line segment, endpoint, ratio
Template created by Region 1 ESA
Page 6 of 8
Geometry Math Tool Unit 4
Unit 4: Connecting Algebra and Geometry Through Coordinates G.GPE.7
Cluster: Use coordinates to prove simple geometric theorems algebraically.
Standard
Instructional Notes: G.GPE.7 provides practice with the
distance formula and its connection with the Pythagorean
theorem.
G.GPE.7 Use coordinates to compute perimeters of polygons
and areas of triangles and rectangles, e.g., using the distance
formula.★
Directly
Somewhat
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Aligned
Aligned
Content/Skills Included in Textbook
(Include page numbers and comments)
Suggested Learning Targets

I can use the coordinates of the vertices of a
polygon graphed in the coordiante plane and
use the distance formula to compute the
perimeter.

I can use the coordinates of the vertices of
triangles and rectangles graphed in the
coordiante plane to compute area.
Essential Questions/ Enduring Understandings
 How can algebra be useful when expressing
geometric properties?
Algebra can be used to efficiently and
effectively describe and apply geometric
properties.
Assessment
Assessments align to suggested learning targets.
Directly
Aligned
Somewhat
Aligned
Not
Aligned
Check all assessment types that address this standard





Drill and practice
Multiple choice
Short answer (written)
Performance (verbal explanation)
Product / Project
Vocabulary
Coordinate plane, coordinates, distance formula, perimeter, polygon, area, triangle, rectangle
Template created by Region 1 ESA
Page 7 of 8
Geometry Math Tool Unit 4
Unit 4: Connecting Algebra and Geometry Through Coordinates G.GPE.2
Cluster: Translate between the geometric description and the equation for a conic section.
Standard
Instructional Notes: The directrix should be parallel to a
coordinate axis.

I can define a parabola.

I can find the distance from a point on the
parabola (x, y) to the directrix.

I can find the distance from a point on the
parabola (x, y to the focus using the distance
formula (Pythagoprean Theorem).

I can equate the two distance expressions
for a parabola to write its equation.

I can identify the focus and directrix of a
prabola when given its equation.
Essential Questions
How can algebra be useful when expressing
geometric properties?
G.GPE.2 Derive the equation of a parabola given a focus and
directrix.
Enduring Understandings
Algebra can be used to efficiently and effectively describe and
apply geometric properties.
Directly
Somewhat
Not
Aligned
Aligned
Aligned
Content/Skills Included in Textbook
(Include page numbers and comments)
Suggested Learning Targets

Assessment
Assessments align to suggested learning targets.
Directly
Aligned
Somewhat
Aligned
Not
Aligned
Check all assessment types that address this standard





Drill and practice
Multiple choice
Short answer (written)
Performance (verbal explanation)
Product / Project
Vocabulary
Parabola, focus, directrix, distance formula, factor, perfect square trinomial
Template created by Region 1 ESA
Page 8 of 8