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## Three-Dimensional Figures

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**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.**Space Figures**• Translate a rectangle through space – It creates a rectangular prism!**Space Figures**• Translate a triangle through space – It makes a triangular prism!**Space Figures**• Translate a circle through space – It makes a cylinder!**Space Figures**• Rotate a rectangle around an axis of symmetry – it also makes a cylinder!**Space Figures**• Twirl (rotate) a triangle around one of its sides – It makes a cone!**Space Figures**• Twirl (rotate) a circle around its diameter – It makes a sphere!**Let’s try some examples!**Example 1**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.**Turning Point**• Let’s test your knowledge! Grab your clicker!**1. What is the figure show below called?**• Cone • Cylinder • Cube • Rectangular prism**2. The base of a cylinder is shaped like a ______.**• Rectangle • Square • Triangle • circle**3. What three-dimensional figure will be formed if the**right triangle shown is rotated about the line shown? • Cone • Cylinder • Cube • sphere**4. What three-dimensional figure will be formed if the**rectangle shown is rotated about the line shown? • Cone • Cylinder • Cube • 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? • Cone • Cube • Cylinder • Rectangular prism**6. What three-dimensional figure will be formed if rectangle**ABCD is rotated about AB? • Cone • Cube • Cylinder • prism**Ticket-out-the-door**• What 3D figure is created when you…. • Translate a rectangle • Translate a circle • Rotate a rectangle • Translate a triangle • Rotate a triangle • Rotate a circle • Translate a square**Cross-Sections**EQ: How can I describe the cross-sections of solid figures?**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 1**Describe three different cross-sections you can find for the rectangular prism below**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.**Turning Point**• Let’s test your knowledge! Grab your clicker!**1. The cylinder below is cut by the plane shown. What is**the shape of the cross-section formed? • Circle • Rectangle • Trapezoid • Triangle**2. The cube below is cut by the plane shown. What is the**shape of the cross-section formed? • Circle • Rectangle • Square • triangle**3. Suppose a cone is cut by a plane. Which cross-section is**NOT possible? • Circle • Ellipse • Square • triangle**4. The cross-section of a three-dimensional figure is**shaped like a circle. The three-dimensional figure could NOT be a ________. • Cone • Cylinder • Pyramid • 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? • Parallel to a base of the cylinder • Perpendicular to a base of the cylinder • Slightly tilted away from a base of the cylinder • None of the above