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Graphing Polygons

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Graphing Polygons

Study Guide

Key Definition

A polygon is a closed figure formed by connecting multiple points, called vertices, in a plane. The sides are the line segments connecting these vertices.

Important Notes

To find the distance between two points with the same x-coordinates, use $|y_2 - y_1|$
To find the distance between two points with the same y-coordinates, use $|x_2 - x_1|$
Polygons are named by their vertices, for example, $\triangle ABC$
Opposite sides of a rectangle are congruent and parallel
The sum of the interior angles of a polygon with $n$ sides is $(n-2) \times 180^\circ$

Mathematical Notation

$\angle$ represents an angle

$\triangle$ represents a triangle

$\overline{AB}$ represents line AB

$\cong$ represents congruence

$\sqrt{x}$ represents the square root of x

Remember to use proper notation when solving problems

Why It Works

Graphing polygons involves plotting points and connecting them, allowing us to visually understand relationships between sides and angles by using coordinate geometry.

Remember

Use the distance formula $\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$ to calculate distances in the coordinate plane.

Quick Reference

Distance Formula:$\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$

Polygon Interior Angles:$(n-2) \times 180^\circ$

Understanding Graphing Polygons

Choose your learning level

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Video explanation of this concept

Beginner

Start here! Easy to understand

Beginner Explanation

When graphing polygons, start by plotting each vertex's coordinates on the plane and then connect them in order to form the shape. For example, a triangle with vertices (0,0), (2,0), and (1,2) is drawn by plotting these points and drawing line segments between them.

Practice Problems

Test your understanding with practice problems

Quick Quiz

Single Choice Quiz

Beginner

What is the distance between points $(1, 2)$ and $(1, 6)$?

Real-World Problem

Question Exercise

Intermediate

Teenager Scenario

Imagine you're designing a triangular park with vertices at A(1,2), B(1,6), and C(-4,2). Calculate the length of each side AB, BC, and AC.

Thinking Challenge

Thinking Exercise

Intermediate

Think About This

Can you find the fourth vertex of a rectangle if three vertices are $(2, 3)$, $(2, 7)$, and $(6, 3)$?

Challenge Quiz

Single Choice Quiz

Advanced

Find the length of diagonal $\overline{AC}$ in a rectangle with vertices A(0,0), B(0,5), C(8,5), and D(8,0).

Recap

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Review key concepts and takeaways