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TABLE OF CONTENTS Lessons Lesson 1. Introduction to Geometry..... 7 Lesson 2. Naming Plane and Solid Shapes.... 10 Lesson 3. Dimensions of Shapes. 18 Lesson 4. Vertices, Edges and Faces..... 23 Lesson 5. Polygons..... 32 Lesson 6. Identifying Plane and Solid Shapes... 34 Lesson 7. Working with Shapes....... 37 Worksheets Lesson 1 Worksheet Introduction to Geometry 41 Lesson 2 Worksheet Naming Plane and Solid Shapes.. 44 Lesson 3 Worksheet Dimensions of Shapes 47 Lesson 4 Worksheet Vertices, Edges and Faces 50 Lesson 5 Worksheet Polygons... 53 Lesson 6 Worksheet Identifying Plane and Solid Shapes.... 56 Lesson 7 Worksheet Working with Shapes...... 59 Worksheets Solution Guides Lesson 1 Worksheet Introduction to Geometry 65 Lesson 2 Worksheet Naming Plane and Solid Shapes.. 72 Lesson 3 Worksheet Dimensions of Shapes 78 Lesson 4 Worksheet Vertices, Edges and Faces 86 Lesson 5 Worksheet Polygons... 92 Lesson 6 Worksheet Identifying Plane and Solid Shapes.... 98 Lesson 7 Worksheet Working with Shapes...... 104 www.aplustutorsoft.com Page 6 of 110
Lesson 1 Introduction to Geometry Do you like to draw pictures or play with legos? If so, then you will like geometry. Geometry is the study of shapes. There are two kinds of shapes; plane shapes and solid shapes. Plane shapes are flat shapes, as if you were drawing on paper. These are examples of plane shapes, which we will learn more about in later sections: a point, a line, a circle, a triangle, a rectangle and a square. www.aplustutorsoft.com Page 7 of 110
Those are the plane shapes. Now let s look at some solid shapes. Legos are solid shapes. If a shape looks like it can be filled, then it s a solid shape. Do you see how it looks like we can fill up this cylinder? We often use cylinders to measure liquids, like water. These are examples of the solid shapes we are going to learn more about: a sphere, a cone, a pyramid, a cylinder, a rectangular prism and a cube. www.aplustutorsoft.com Page 8 of 110
In geometry, we study the properties of shapes. For example, we can describe shapes by how many dimensions they have. Shapes can have 0, 1, 2 or 3 dimensions. We can also describe shapes by how many vertices, edges and faces they have. We will learn more about these properties in the next sections. Geometry is everywhere; in our food, our toys, our houses, our cars and so much more. You will likely use geometry in your adult careers. Geometry can be a lot of fun and you will learn more in this chapter and as you take higher level math courses. www.aplustutorsoft.com Page 9 of 110
Lesson 2 Naming Plane and Solid Shapes Geometry is the study of shapes. There are two kinds of shapes; plane shapes and solid shapes. Plane shapes are flat shapes, as if you were drawing on paper. The plane shapes we are going to learn about are: a point, a line, a circle, a triangle, a rectangle and a square. Solid shapes look as though you can fill it up with something, like water or air. The solid shapes we are going to learn about are: a sphere, a cone, a pyramid, a cylinder, a rectangular prism and a cube. www.aplustutorsoft.com Page 10 of 110
Now, I am going to show you a shape and you tell me what shape it is. Ready? Great job! This is a circle. Is a circle a plane shape or a solid shape? Excellent! A circle is a plane shape because it is flat. Right! This is a square. Is a square a plane shape or a solid shape? www.aplustutorsoft.com Page 11 of 110
Very good! A square is a plane shape because it is flat. Right! This is a point. Is a point a plane shape or a solid shape? Yes! A point is a plane shape. Great job! This is a line. Is a line a plane shape or a solid shape? Excellent! A line is a plane shape. www.aplustutorsoft.com Page 12 of 110
Fantastic! This is a rectangle. Is a rectangle a plane shape or a solid shape? Great! A rectangle is a plane shape because it is flat. Right! This is a triangle. Is a triangle a plane shape or a solid shape? You are doing great! Keep it up! A triangle is a plane shape. www.aplustutorsoft.com Page 13 of 110
Super job! This is a sphere. Is a sphere a plane shape or a solid shape? Yes! A sphere is a solid shape because you can fill it up with something. Fantastic! This is a cone. Is a cone a plane shape or a solid shape? www.aplustutorsoft.com Page 14 of 110
Great! A cone is a solid shape because you can fill it up. Fabulous! This is a cube. Is a cube a plane shape or a solid shape? Right! A cube is a solid shape because you can fill it up. Fabulous job! This is a cylinder. Is a cylinder a plane shape or a solid shape? www.aplustutorsoft.com Page 15 of 110
Very good! A cylinder is a solid shape because you can fill it up with something. Great job! This is a rectangular prism. Is a rectangular prism a plane shape or a solid shape? Excellent! A rectangular prism is a solid shape. www.aplustutorsoft.com Page 16 of 110
Great job! This is a pyramid. Is a pyramid a plane shape or a solid shape? Very good! A pyramid is a solid shape. You did a fabulous job naming plane and solid shapes. If you need more help, please go back and review this lesson again. www.aplustutorsoft.com Page 17 of 110
Lesson 3 Dimensions of Shapes Plane shapes and solid shapes can be described by how many dimensions they have. A dimension is basically a line that goes in one direction. For example, this juice box has 3 lines going in different directions, which are labeled length, width and height. So, this juice box has 3 dimensions and is called a 3-dimensional shape. A shape can have 0, 1, 2 or 3 dimensions. To determine how many dimensions a shape has, we must determine how many lines the shape has. www.aplustutorsoft.com Page 18 of 110
Let s start with a 0-dimensional shape. If a shape has 0 dimensions, then it cannot have length, width or height. Therefore, the only 0-dimensional shape is a point because a point does not have any lines. In Geometry, a point is not a thing, but a place or a specific location in space. A line is a collection of points along a straight path that goes on forever in both directions. A line only has length, not width or height. Since it only has one dimension, a line is a 1-dimensional shape. How many dimensions does a square have? How about a square, how many dimensions does a square have? Fabulous! A square has 2 lines, length and width, therefore a square is a 2-dimensional shape. Shapes that have 2 dimensions have length and height or if we lay it flat, length and width. We use width to describe one of the lines in the rectangle here because it is a plane shape, which is a flat shape. www.aplustutorsoft.com Page 19 of 110
All plane shapes have 0, 1 or 2-dimensions. All solid shapes have 3 dimensions; length, width and height. So, this is what our chart looks like now. Let s practice identifying how many dimensions shapes have. www.aplustutorsoft.com Page 20 of 110
How many dimensions do you think a rectangular prism has? You are doing great! A rectangular prism has 3 dimensions; length, width and height. Therefore a rectangular prism is a 3-dimensional shape. How many dimensions does a triangle have? Right! A triangle has length and height, but no width. So, a triangle has 2 lines, or 2 dimensions. Therefore, a triangle is a 2-dimensional shape. How many dimensions do you think a pyramid has? You are doing great! A pyramid has 3 dimensions; length, width and height. Therefore, a pyramid is a 3-dimensional shape. Which shape below has 2 dimensions? Right! A square has 2 dimensions; length and width. Which shape below has 3 dimensions? Right! A cone has 3 dimensions; length, width and height. www.aplustutorsoft.com Page 21 of 110
Which shape below has 3 dimensions? Right! A cylinder has 3 dimensions; length, width and height. Which shape below has 2 dimensions? Right! A rectangle has 2 dimensions; length and width. Which shape below has 3 dimensions? Right! A sphere has 3 dimensions; length, width and height. You did a fantastic job identifying 0, 1, 2 and 3 dimensional shapes. If you need more help, please go back and review this lesson again. www.aplustutorsoft.com Page 22 of 110
Lesson 4 Vertices, Edges and Faces We have learned we can identify shapes by how many dimensions they have. We can also identify them by other properties, such as how many vertices, edges and faces they have. Let s start with how many vertices shapes have. Vertices is plural for vertex. A vertex is the corner where 2 or more lines meet. If we draw another line here, what shape did we make? www.aplustutorsoft.com Page 23 of 110
Yes! It is a triangle. Now how many vertices do you see? Excellent! A triangle has 1, 2, 3 vertices. So, one corner is a vertex and 2 or more corners are called vertices. How many vertices does a square have? www.aplustutorsoft.com Page 24 of 110
Excellent, 4! Count them with me, 1, 2, 3, 4. Great job! A square has 4 vertices. How many vertices does a cube have? Let s find how many vertices a cube has. Count them with me, please. Ready? 1, 2, 3, 4, 5, 6, 7, 8. A cube has 8 vertices. How many vertices does a pyramid have? Excellent job! Let s count the vertices together: 1, 2, 3, 4, 5. A pyramid has 5 vertices. www.aplustutorsoft.com Page 25 of 110
Now we know that a vertex is the corner where 2 or more lines meet. Do you have any idea what the edge could be? Let s find an edge on a triangle. This is an edge. An edge is a line or one side of the shape. Can you tell me how many edges a triangle has? A triangle has more than 1 edge. Can you tell me how many edges a triangle has? Fabulous! A triangle has 1, 2, 3 edges. www.aplustutorsoft.com Page 26 of 110
How many edges does a square have? Excellent, 4! Count them with me, 1, 2, 3, 4. Great job! A square has 4 edges. How many edges does a pyramid have? Let s find how many edges a pyramid has. Count them with me, please. Ready? 1, 2, 3, 4, 5, 6, 7, 8. A pyramid has 8 edges. How many edges does a cube have? www.aplustutorsoft.com Page 27 of 110
Excellent job! Let s count the edges together: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12. A cube has 12 edges. We know that a vertex is the corner where 2 or more lines meet. And now we know that an edge is a line or one side of the shape. Do you have any idea what the face of a shape could be? Let s find a face on a triangle. This is a face. A face is the flat surface of a shape. So, a triangle has 1 face. www.aplustutorsoft.com Page 28 of 110
In fact, all plane 2-dimesional shapes have 1 face because they are all flat shapes. What about 3-dimensional shapes? How many faces does a cube have? Right! Notice how a square is a face of the cube. It takes 1, 2, 3, 4, 5, 6 squares to make a cube. So, a cube has 6 faces. How many faces does a pyramid have? www.aplustutorsoft.com Page 29 of 110
Right, a pyramid has 5 faces. Notice how a triangle is a face of the pyramid. There is also a square that makes the base of the pyramid. So, it takes 1, 2, 3, 4 triangles to make a pyramid and 1 square to make a pyramid. So, a pyramid has 5 faces. So, we have learned that a vertex is the corner where 2 or more lines meet, an edge is a line or a side of the shape and a face is the flat surface of the shape. How many vertices does a cone have? Excellent job! A cone has only 1 vertex at the top. How many edges does a sphere have? www.aplustutorsoft.com Page 30 of 110
Excellent job! A sphere has 0 edges. How many faces does a circle have? Right, a circle has 1 face. How many edges does a cylinder have? Excellent job! A cylinder has 0 edges. You did a great job! If you need more help finding vertices, edges and faces of shapes, please go back and review this lesson again. www.aplustutorsoft.com Page 31 of 110
Lesson 5 Polygons Polygons are 2-dimensional plane shapes. All of these shapes are polygons. A polygon has many straight sides that connect to one another making a closed shape. These shapes are not polygons. Can you tell me why? Polygons cannot have curves, just straight sides. So, all of the shapes with curves are not polygons. This includes the circle and oval. Polygons also have to be closed shapes. These two shapes are open, so they are not polygons. Now, I am going to show you some pictures and you tell me if they are a polygon or not. Ready? Okay. Is this a polygon? Yes, this is a polygon because it is has straight sides that make a closed shape. Great job! www.aplustutorsoft.com Page 32 of 110
Is this a polygon? Very good. This is not a polygon because it is has curves and a polygon has straight sides only. Is this a polygon? You got it; this is not a polygon because it is not a closed shape. Is this a polygon? Yes, this is a polygon because it is has straight sides that make a closed shape. Great job! Is this a polygon? You got it; this is not a polygon because it is not a completely closed shape. Is this a polygon? Yes, this is a polygon because it is has straight sides that make a closed shape. Great job! You did a great job identifying polygons. If you need more practice, feel free to review this lesson again. www.aplustutorsoft.com Page 33 of 110
Lesson 6 Identifying 2 and 3-Dimensional Shapes Geometric shapes are all around us. We can find shapes in the toys we play with, the food we eat and all kinds of things we use every day. Let s practice identifying 2 and 3-dimensional shapes. Which one of these is the shape of a circle? Excellent job! The dime is the shape of a circle. Which one of these is the shape of a rectangle? Excellent job! The dollar bill is the shape of a rectangle. Which one of these is the shape of a cube? Excellent job! The ice cubes are the shape of a cube. Which one of these is the shape of a triangle? www.aplustutorsoft.com Page 34 of 110
Excellent job! The yield sign is the shape of a triangle. Which one of these is the shape of a sphere? Excellent job! The orange is the shape of a sphere. Which one of these is the shape of a cylinder? Excellent job! The can is the shape of a cylinder. Which one of these is the shape of a cone? Excellent job! The birthday hat is the shape of a cone. www.aplustutorsoft.com Page 35 of 110