## Unit 8

ALGEBRAIC CONNECTIONS TO GEOMETRIC CONCEPTS

**UNIT DESCRIPTION**

In this unit, students will solve problems involving distance, midpoint, slope, area, and perimeter to model and explain real-life phenomena. Students will learn how to do the following:

● Derive the distance formula through the use of Pythagorean theorem.

● Use coordinates, slope relationships, and distance formula to prove simple geometric theorems algebraically.

● Compute the perimeters of polygons using the coordinates of the vertices and the distance formula.

● Find the areas of rectangles and triangles using the coordinates of the vertices and the distance formula.

● Show that the slopes of parallel lines are the same.

● Show that the slopes of perpendicular lines are opposite reciprocals.

● Given the equation of a line and a point not on the line, find the equation of the line that passes through the point and is parallel/perpendicular to the given line.

In this unit, students will learn the relationships between slopes of parallel lines and between perpendicular lines and then use those relationships to write the equations of lines. They will also extend the use of the Pythagorean Theorem to the coordinate plane to introduce students to the distance formula, revisit definitions of polygons while using slope and distance on the coordinate plane and use knowledge of algebra and geometry concepts to find the area and perimeter of defined figures. In the end, students will solve problems involving distance, midpoint, slope, area, and perimeter to model and explain real-life phenomena.

● Derive the distance formula through the use of Pythagorean theorem.

● Use coordinates, slope relationships, and distance formula to prove simple geometric theorems algebraically.

● Compute the perimeters of polygons using the coordinates of the vertices and the distance formula.

● Find the areas of rectangles and triangles using the coordinates of the vertices and the distance formula.

● Show that the slopes of parallel lines are the same.

● Show that the slopes of perpendicular lines are opposite reciprocals.

● Given the equation of a line and a point not on the line, find the equation of the line that passes through the point and is parallel/perpendicular to the given line.

In this unit, students will learn the relationships between slopes of parallel lines and between perpendicular lines and then use those relationships to write the equations of lines. They will also extend the use of the Pythagorean Theorem to the coordinate plane to introduce students to the distance formula, revisit definitions of polygons while using slope and distance on the coordinate plane and use knowledge of algebra and geometry concepts to find the area and perimeter of defined figures. In the end, students will solve problems involving distance, midpoint, slope, area, and perimeter to model and explain real-life phenomena.

**LEARNING TARGETS**

- I can use distance and midpoint formula to solve real-world phenomena.
- I can identify the rate of change of parallel and perpendicular lines.
- I can connect parallel and perpendicular lines to real-world phenomena.
- I can use distance and midpoint formula to calculate area and perimeter 2-deminsional shapes on a coordinate plane.
- I can apply area and perimeter of 2-demisional shapes on a coordinate plane to solve real-world phenomena.

**TEXTBOOK CONNECTIONS**

Distance on Coordinate Plane- Geometry Course Module 1 Lesson 4 Examples 3 and Example 4

Midpoint Formula- Geometry Course Module 1 Lesson 7

Area and Perimeter of 2-dimensional shapes- Geometry Course Module 2 Lesson 3

Parallel and Perpendicular Lines- Algebra 1 Course Module 5 Lesson 2

Midpoint Formula- Geometry Course Module 1 Lesson 7

Area and Perimeter of 2-dimensional shapes- Geometry Course Module 2 Lesson 3

Parallel and Perpendicular Lines- Algebra 1 Course Module 5 Lesson 2

**IXL SKILLS**

__Distance on Coordinate Plane:__

- ALGEBRA 1- G.4
- GEOMETRY- B.13

__Midpoint:__

- ALGEBRA 1- G.2, G.3
- GEOMETRY- B.10

__Area and Perimeter:__

- GEOMETRY- S.6, S.7

__Parallel and Perpendicular Lines:__

- ALGEBRA 1- T.27, T.28
- GEOMETRY- E.5, E.6