HSG-GPE.B.4

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- HSG-GPE.B.4Use 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).
- HSG-GPE.B.5Prove 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).
- HSG-GPE.B.6Find the point on a directed line segment between two given points that partitions the segment in a given ratio.
- HSG-GPE.B.7Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.*

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HSG-GPE.B.5

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- HSG-GPE.B.4Use 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).
- HSG-GPE.B.5Prove 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).
- HSG-GPE.B.6Find the point on a directed line segment between two given points that partitions the segment in a given ratio.
- HSG-GPE.B.7Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.*

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## HSG-GPE.B.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).

19 Lesson(s)

Big Idea:

#### In this student-centered lesson, students work together to construct parallel and perpendicular lines while also writing equations for these lines.

Standards:

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(39)

Reflections
(5)

### Graphing Parallel and Perpendicular Lines (Day 2 of 2)

Algebra I »
Unit: Graphing Linear Functions

Algebra I »
Unit: Graphing Linear Functions

Big Idea:

#### Students will connect the main ideas from the previous four lessons to write the equations of parallel and perpendicular lines using given information.

Standards:

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(34)

Resources
(17)

Reflections
(2)

### Get Perpendicular with Geoboards!

Algebra I »
Unit: Linear Functions

Algebra I »
Unit: Linear Functions

Big Idea:

#### Students reason about Perpendicular Lines with simple concrete examples using Geoboards and extend their reasoning to designing parking lines.

Standards:

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(2)

Resources
(17)

Reflections
(1)

### Tools of Geometry Unit Assessment

Geometry »
Unit: Tools of Geometry

Geometry »
Unit: Tools of Geometry

Big Idea:

#### Test time! Students take the first unit assessment, aligned to the Common Core standards for this unit.

Standards:

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### Equations for Parallel and Perpendicular Lines.

Algebra I »
Unit: Linear Functions

Algebra I »
Unit: Linear Functions

Big Idea:

#### For students to write the equation of a line parallel to or perpendicular to a line and passing through a given point using different representations of linear functions.

Standards:

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(1)

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(12)

Big Idea:

#### The emphasis in this lesson is that students not only know the definition of parallel lines, but why lines are parallel.

Standards:

Resources
(9)

### Graphing Parallel and Perpendicular Lines (Day 1 of 2)

Algebra I »
Unit: Graphing Linear Functions

Algebra I »
Unit: Graphing Linear Functions

Big Idea:

#### Through graphing students will deduce that the slopes of parallel lines are the same and the slopes of perpendicular lines are opposite reciprocals.

Standards:

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(26)

Resources
(16)

Reflections
(2)

### Coordinate Geometry Unit Review and Test

Geometry »
Unit: Coordinate Geometry

Geometry »
Unit: Coordinate Geometry

Big Idea:

#### Test time! Students review and then take the unit assessment, hopefully demonstrating their knowledge of coordinate geometry, as well as their ability to organize and justify their work.

Standards:

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(5)

Resources
(14)

### More Practice with Coordinate Geometry

Geometry »
Unit: Coordinate Geometry

Geometry »
Unit: Coordinate Geometry

Big Idea:

#### Students put their coordinate geometry knowledge to work, investigating characteristics of geometric figures and proving hypotheses.

Standards:

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(4)

Resources
(9)

Big Idea:

#### Students will complete review questions from the current unit as well as practice their pacing when answering assessment questions.

Standards:

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(8)

Resources
(16)

Reflections
(1)

Big Idea:

#### Students will fold away to discover the relationship between a focus, directrix and parabola as well as play Jeopardy to review key topics in Line-sanity unit including alternate interior angles.

Standards:

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Resources
(22)

Reflections
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Big Idea:

#### Algebra and geometry intersect, please pardon the pun, in this lesson on perpendicular bisectors.

Standards:

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Resources
(23)

Reflections
(2)

Big Idea:

#### Around the world time! Students will travel around the classroom to review and then present their review questions to each other for review!

Standards:

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(2)

Resources
(14)

Reflections
(2)

### Exploring Our Concepts with Dynamic Geometry Software

Geometry »
Unit: Coordinate Geometry

Geometry »
Unit: Coordinate Geometry

Big Idea:

#### What is a strategic use of tools? Let's use dynamic software to deepen our students' understanding of coordinate geometry!

Standards:

Favorites
(3)

Resources
(20)

Reflections
(2)

Big Idea:

#### Challenge students with this unit test or problem set covering perp and parallel lines, perp bisectors and many more line related topics

Standards:

Resources
(8)

Reflections
(1)

Common Core Math

### Kindergarten

### First Grade

### Second Grade

### Third Grade

### Fourth Grade

### Fifth Grade

### Sixth Grade

### Seventh Grade

### HS Number & Quantity

### HS Algebra

### HS Functions

### HS Geometry

### Kindergarten

### First Grade

### Second Grade

### Third Grade

### Fourth Grade

### Fifth Grade

### Sixth Grade

### Seventh Grade

### Eighth Grade

### Ninth and Tenth Grade

### Kindergarten

### First grade

### Second grade

### Third Grade

### Fourth grade

### Fifth grade

### Middle School

Kindergarten

First Grade

Second Grade

Third Grade

Fourth Grade

Fifth Grade

Sixth Grade

Seventh Grade

HS Number & Quantity

HS Algebra

HS Functions

HS Geometry

Kindergarten

First Grade

Second Grade

Third Grade

Fourth Grade

Fifth Grade

Sixth Grade

Seventh Grade

Eighth Grade

Ninth and Tenth Grade

Kindergarten

First grade

Second grade

Third Grade

Fourth grade

Fifth grade

Middle School