Vocabulary
• Two-dimensional figures (plane figures) – triangles, quadrilaterals, and circles. They lie in one plane
Vocabulary• Three-dimensional figures – figures that
have length, width, and depth• Cone
• Cylinder
• Prism
• Pyramid
• Sphere
• Two-dimensional figures can be transformed through space to create three-dimensional figures. One way is to rotate a two-dimensional figure about a line. This line is sometimes called an axis of symmetry.
Example 3
A square measures 1 inch on each side. Suppose a copy of the square is translated 2 inches directly above the plane in which it lies to form a second square. The two squares are then connected with four line segments. Describe the three-dimensional figure that is formed.
1. What is the figure show below called?
1 2 3 4
25% 25%25%25%1. Cone
2. Cylinder
3. Cube
4. Rectangular prism
2. The base of a cylinder is shaped like a ______.
1 2 3 4
25% 25%25%25%1. Rectangle
2. Square
3. Triangle
4. circle
3. What three-dimensional figure will be formed if the right triangle shown is rotated
about the line shown?
1 2 3 4
25% 25%25%25%1. Cone
2. Cylinder
3. Cube
4. sphere
4. What three-dimensional figure will be formed if the rectangle shown is rotated
about the line shown?
1 2 3 4
25% 25%25%25%1. Cone
2. Cylinder
3. Cube
4. sphere
5. A rectangle is translated 3 inches directly above the plane in which it lies. The vertices of the two rectangles are
then connected with four line segments. What three-dimensional figure is formed?
1 2 3 4
25% 25%25%25%1. Cone
2. Cube
3. Cylinder
4. Rectangular prism
6. What three-dimensional figure will be formed if rectangle ABCD is rotated about
AB?
1 2 3 4
25% 25%25%25%1. Cone
2. Cube
3. Cylinder
4. prism
Ticket-out-the-door
• What 3D figure is created when you….1. Translate a rectangle2. Translate a circle3. Rotate a rectangle4. Translate a triangle5. Rotate a triangle6. Rotate a circle7. Translate a square
Vocabulary
• Cross-section – a view of the inside of a 3D figure after it is sliced
• Polyhedron – a 3D figure (a solid with flat faces)
http://www.learner.org/channel/courses/learningmath/geometry/session9/part_c/index.html
Example 2
The cylinder below sits on a horizontal base. Draw and describe the cross-section formed when the cylinder is cut by a plane that is tilted away from its base.
Solution
• The cross-section is shaped like an oval. In mathematics, this shape is called an ellipse.
Example 3
• The cone below sits on a horizontal base. Draw and describe the cross-sections formed when the cone is cut by a vertical plane through its vertex.
Solution
• The cross-section is shaped like an isosceles triangle. The base of the triangle is on the base of the cone.
Example 4
• The pyramid below has a square horizontal base. Draw and describe the cross-sections formed when the cone is cut by a vertical plane that does not pass through the vertex at its top.
Solution
• The cross-section will be shaped like a quadrilateral. This figure is called an isosceles trapezoid.
1. The cylinder below is cut by the plane shown. What is the shape of the cross-
section formed?
1 2 3 4
25% 25%25%25%1. Circle
2. Rectangle
3. Trapezoid
4. Triangle
2. The cube below is cut by the plane shown. What is the shape of the cross-
section formed?
1 2 3 4
25% 25%25%25%1. Circle
2. Rectangle
3. Square
4. triangle
3. Suppose a cone is cut by a plane. Which cross-section is NOT possible?
1 2 3 4
25% 25%25%25%1. Circle
2. Ellipse
3. Square
4. triangle
4. The cross-section of a three-dimensional figure is shaped like a circle. The three-
dimensional figure could NOT be a ________.
1 2 3 4
25% 25%25%25%
1. Cone
2. Cylinder
3. Pyramid
4. sphere
5. A cylinder is cut by a plane to form a cross section shaped like an ellipse. How could the
plane that formed the cross-section have cut the cylinder?
1 2 3 4
25% 25%25%25%1. Parallel to a base of the cylinder
2. Perpendicular to a base of the cylinder
3. Slightly tilted away from a base of the cylinder
4. None of the above