Unit 8 — Geometry, Measurement, and Coordinate Graphs

Welcome back!

Geometry helps us describe the shapes, sizes, positions, and relationships of objects.

Builders use geometry to construct homes.

Engineers use geometry to design bridges.

Scientists use geometry to describe patterns found in nature.

Today you will strengthen your understanding of geometry while learning how mathematics describes the world around us.

Points, Lines, and Angles

Geometry begins with simple ideas.

A point represents an exact location.

A line extends forever in both directions.

A line segment has two endpoints.

A ray begins at one point and extends forever in one direction.

Angles are formed when two rays share a common endpoint.

Classifying Angles

Angles are measured in degrees (°).

Common types include:

• acute (less than 90°)
• right (exactly 90°)
• obtuse (greater than 90° but less than 180°)
• straight (180°)

Learning to identify angles helps us understand many geometric figures.

Classifying Triangles

Triangles can be classified by their sides.

• equilateral (three equal sides)
• isosceles (two equal sides)
• scalene (no equal sides)

They can also be classified by their angles.

• acute triangle
• right triangle
• obtuse triangle

Understanding these properties helps us describe geometric figures accurately.

Quadrilaterals

A quadrilateral has four sides.

Examples include:

• square
• rectangle
• parallelogram
• rhombus
• trapezoid

Each has its own unique properties.

Learning these properties helps us compare shapes.

Perimeter and Area

Perimeter is the distance around a figure.

Area measures the surface inside a figure.

Examples:

Rectangle

Perimeter:

2 × (length + width)

Area:

length × width

Always include the correct units in your answers.

Volume

Volume measures the amount of space inside a three-dimensional object.

For a rectangular prism:

Volume = length × width × height

Volume is measured in cubic units.

Examples include:

• cubic centimeters
• cubic meters
• cubic inches

Coordinate Graphs

A coordinate graph helps us locate points.

The horizontal axis is called the x-axis.

The vertical axis is called the y-axis.

A point is written as an ordered pair.

Example:

(4, 2)

This means:

• move 4 units right
• move 2 units up

Coordinate graphs are used in science, engineering, navigation, and computer graphics.

Solving Real-World Problems

Geometry helps solve practical problems.

Examples include:

• finding the amount of paint needed for a wall
• measuring land
• planning gardens
• designing buildings
• creating maps

Careful measurement and calculation lead to accurate solutions.

Activity

Draw:

• three different triangles
• four different quadrilaterals

Measure their sides and angles.

Then calculate:

• perimeter
• area (when appropriate)

Finally, plot ten points on a coordinate grid and connect them to create a geometric design.

Practice

Answer these questions.

What is the difference between a line and a line segment?

Name the four common types of angles.

How can triangles be classified?

What is the difference between perimeter and area?

What does volume measure?

How is a coordinate pair written?

Review

Today you learned:

• geometry describes shapes and space
• triangles and quadrilaterals can be classified by their properties
• perimeter, area, and volume measure different quantities
• coordinate graphs locate positions precisely
• geometry has many practical applications

Geometry helps us understand and design the world around us.

Looking Ahead

Next we will investigate patterns, variables, introductory algebra, and mathematical relationships, preparing for the more advanced mathematics you will study in middle school.