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.6

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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.6

## Find the point on a directed line segment between two given points that partitions the segment in a given ratio.

2 Lesson(s)

### Segments First

Geometry »
Unit: Introduction to Geometry: Points, Lines, Planes, and Angles

Geometry »
Unit: Introduction to Geometry: Points, Lines, Planes, and Angles

Big Idea:

#### Students will measure, measure, measure to discover properties of segments.

Standards:

Favorites
(13)

Resources
(26)

Reflections
(3)

### Partitioning Segments in the Coordinate Plane

Geometry »
Unit: Analytic Geometry

Geometry »
Unit: Analytic Geometry

Big Idea:

#### 'Howdy Partishner'...In this lesson, students will use analytic geometry to define the coordinates of partitioning points.

Standards:

Favorites
(34)

Resources
(25)

Reflections
(2)

Common Core Math

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### 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