This fourth grade geometry lesson teaches the definitions for a line, ray, angle, acute angle, right angle, and obtuse angle. We also study how the size of the angle is ONLY determined by how much it has 'opened' as compared to the whole circle. The lesson contains many varied exercises for students.
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Our circle solver lets you find the area, diameter or circumference of a circle, given one value is known. Enter the area, diameter or circumference of a circle and it will solve for the other two. Area: Diameter: Circumference: Other Calculators.
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- When we first introduce angles, we can immediately draw the connection between angles and circles. This is a rich and interesting relationship, and because we are drawing circles and angles, and measuring them numerically at the same time, we can clearly see the relationship between the numbers and the drawings.
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A line has no beginning point or end point. Imagine it continuing indefinitely in both directions. We can name a line using two points on it. This is line EF or line (note the arrowheads). | ||||
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What is an angle? Many people think that an angle is some kind of That point is called the vertex and the two rays are called the sides To name an angle, we use three points, listing the vertex in the middle. |
1. Write if each figure is a line, ray, line segment, or an angle, and name it.
Download beethoven violin sonata 4 program notes. a. _______________________ | b. _______________________ | c. _______________________ |
d. _______________________ | e. _______________________ | f. _______________________ |
2. a. Find the angle formed by the rays DE and DF.
How do we name it?
b. Find the angle formed by the rays CA and CE.
How do we name it?
c. What is BD? (a line, a line segment, or a ray)?
3. a. Draw two points, D and E. Then draw line DE.
b. Draw point Q not on the line.
c. Draw rays DQ and EQ.
d. Find angles EDQ and DEQ in your drawing.
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If the angle opens up to a full | This angle is half of the full circle, Your two pencils (rays) are lying | Download the martian audiobook free. This is one-fourth of the This is called the right | |
In each of these pictures the angle is opened more and more and keeps getting bigger. The arc of the circle is larger. These angles are acute angles, which means they are less than a right angle (less than 90°). Think of acute angles as sharp angles. If someone stabbed you with the vertex of an acute angle, it would feel sharp. | |||
Here's another way of thinking about angles. Think of a sun rising in the morning in the horizon, gradually getting higher, and traveling through the sky along an arc of a circle. |
How big is the angle? It does not matter how long the sides of the angle are. Remember, they are rays, and rays go on indefinitely. But when we draw them on paper, we have to draw them as ending somewhere. The sides of the angle might even seem to have different lengths. That doesn't matter either. The size of the angle is ONLY determined by how much it has “opened” as compared to the whole circle. Think how big an arc of a circle the sides have drawn, as compared to a whole circle. | ||
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4. Which angle is bigger?
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5. a. Sketch three different
acute angles.
b. Sketch three different
obtuse angles.
c. Sketch a right angle
and a straight angle.
6. Label the angles as acute, right, obtuse, or straight. To help, make these angles with two pencils,
checking how much you need to open up the angle.
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7. A triangle has three angles. In fact, the word tri-angle means a three-angled shape.
Which of the triangles a, b, or c has one obtuse angle?
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8. (Optional) Make a geometry notebook where you write down each new term and draw a picture or
pictures that illustrate the term. Use colors and tidy writing. It is like your personal geometry
dictionary. You can also do any drawing problems from the lessons in it. Drawing and writing
yourself, instead of just reading, can help you remember the terms better!
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This lesson is taken from Maria Miller's book Math Mammoth Geometry 1, and posted at www.HomeschoolMath.net with permission from the author. Copyright © Maria Miller.
Math Mammoth Geometry 1
A self-teaching worktext for 4th-5th grade that covers angles, triangles, quadrilaterals, cirlce, symmetry, perimeter, area, and volume. Lots of drawing exercises!
Download ($6.90). Also available as a printed copy.
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