Geometry: A World of Shapes and Figures

1. Geometry: A World of Shapes and Figures Geometry is the branch of mathematics that teaches us about lines, segments, points, rays, angles, and shapes. Geometry is all around us! Can you spot any examples of geometry in our classroom? Created By: 2BrokeTeachers

2. The Basics: Points The most basic geometric figure that exists is called a point. If you were to take your finger and touch your desk, that spot would be a point. If you touch your desk in another spot, that is a point too! Points are everywhere! They can exist completely on their own or they can be part of other geometric figures. Points are usually shown by drawing a very small circle that looks like a period. point point point

3. The Basics: Lines Here are some examples of lines. Can you think of any other examples? Another common geometric figure is a line. Lines are special because they are straight and extend forever and ever in both directions. We show that lines extend forever in both directions by putting arrows on each side of the line.

4. The Basics: Line Segments Sometimes lines can be divided into pieces. These pieces are called line segments. We can tell that a figure is a line segment because it does not extend forever and ever in both directions. Line segments have special points where they stop called “endpoints”. Can you locate the endpoints on the line segment below? Helpful Hints: Did you know that all polygons have sides that are made up of line segments? Take a look at this triangle and count the number of line segments in the figure.

5. The Basics: Rays Lines can also be divided into special geometric figures called rays. A ray is a piece of a line that extends forever and ever in only one direction. The other side of the ray has an endpoint. How do you think we show that a ray extends on forever and ever in one direction? Only one of the objects below is a ray. Can you identify the ray? Explain to a neighbor how you know.

6. The Basics: Angles 105° Two rays that share an endpoint form an angle. Angles come in all shapes and sizes. The distance from one side of an angle to the opposite side of the angle is measured in degrees. There are angles everywhere! Can you spot any angles in our classroom?

7. Types of Angles Obtuse Angle Right Angle There are three different types of angles: right angles, acute angles, and obtuse angles. Every angle can be identified as one of these three types of angles. Acute Angle Look carefully at the three angles above. What do you think makes them different?

8. Types of Angles Obtuse Angle > 90° Acute Angle <90° Right Angle=90° Angles can be identified as right, acute, or obtuse using their measurements. Any angle that is exactly 90° is a right angle. An angle that is less than 90° is an acute angle. An angle that is greater than 90° is an obtuse angle. Helpful Hints: Make an “L” shape with your hand. This is a right angle. Any angle that will fit inside of the “L” will be an acute angle. Any angle that will not fit inside of the “L” will be obtuse. Try it out!

9. Let’s Review… B. A. Which of the following objects is a line? C. Answer choice “B” is correct because the figure is straight and extends in both directions forever.

10. Let’s Review… A. Which of the following objects is a line segment? B. C. Answer choice “A” is correct because the figure is straight and has two endpoints.

11. Let’s Review… A. B. C. Which of the following angles is obtuse? Answer choice “C” is correct because the angle is greater than 90°.