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.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).

14 Lesson(s)

### Becoming More Familiar with the Rules for Transformations

Geometry »
Unit: Transformations

Geometry »
Unit: Transformations

Big Idea:

#### Name that transformation! Students will work at identifying transformations performed upon geometric figures.

Standards:

Favorites
(14)

Resources
(22)

Reflections
(2)

### 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:

Favorites
(8)

Resources
(13)

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)

### 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:

Favorites
(5)

Resources
(14)

### The Basics of Coordinate Geometry

Geometry »
Unit: Coordinate Geometry

Geometry »
Unit: Coordinate Geometry

### 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:

Favorites
(3)

Resources
(9)

Big Idea:

#### Time for the unit review and pulling all of the concepts together!

Standards:

Favorites
(4)

Resources
(24)

Reflections
(3)

### 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)

### Using Coordinates to Prove a Quadrilateral is a Parallelogram

Geometry »
Unit: Quadrilaterals

Geometry »
Unit: Quadrilaterals

Big Idea:

#### Impostors beware! In this lesson students learn to distinguish the real parallelograms from the pretenders.

Standards:

Favorites
(1)

Resources
(11)

Reflections
(1)

Big Idea:

#### This is a comprehensive assessment of all content learned to date.

Standards:

Favorites
(1)

Resources
(12)

Reflections
(1)

### End of Year Alternate Assessment

Geometry »
Unit: Final Assessment

Geometry »
Unit: Final Assessment

Big Idea:

#### In this lesson, students complete a performance task based on paintings by Vasily Kandinsky as an alternative to a final exam or an extra credit assignment.

Standards:

Resources
(5)

### End of Year Assessment Review Day 3 of 4

Geometry »
Unit: Final Assessment

Geometry »
Unit: Final Assessment

Big Idea:

#### In this lesson, students practice problems involving concepts from the units on similarity, trigonometry and coordinate geometry.

Resources
(11)

Reflections
(1)

Big Idea:

#### What's PART backwards and the rest ezoid?...Okay maybe that's too easy...but this lesson on trapezoids is sure to provide a challenge or two.

Standards:

Resources
(12)

Reflections
(1)

### Making Conjectures about the Midsegments of a Triangle

Geometry »
Unit: Developing Logic and Proof

Geometry »
Unit: Developing Logic and Proof

Common Core Math

### Kindergarten

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### Fourth Grade

### Fifth Grade

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### Seventh Grade

### HS Number & Quantity

### HS Algebra

### HS Functions

### HS Geometry

### Kindergarten

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### 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