Three-dimensional figures, or solids, can be made up of flat or curved surfaces. Faces– the polygons that make the polyhedron Edges– A line segment formed by the intersection of 2 faces. Vertices – a point where 3 or more edges meet.

In this lesson, you will learn how to visualize the 2D cross-sections of 3D shapes Cross Section: the 2 dimensional shape that results from cutting through the solid -

Let’s Review Parts of a solid: prism

Core Lesson Effect of slicing plane When a plane intersects the faces, the result will be the edges of a 2D figure The cross section would be a hexagon.

Core Lesson Describe the cross section: The cross section would be a rectangle.

Let’s Review Parts of a solid: pyramid Face, edge, and vertex (vertices)

Core Lesson Identify characteristics of a pyramid: Square Triangles

Vertical, through vertex = triangle

Effect of slicing plane We would see a trapezoid.

Core Lesson Horizontal Cross-section Slices parallel to the base will always be similar to the base

A Common Misunderstanding A plane can slice through a solid in any direction cross-sections are always horizontal or vertical

The Great Pyramids of Giza were originally built with a limestone cap at the top. Over the centuries, these caps have eroded away, and the tops of the pyramids are now parallel to the ground. What 2D shape describes the new top of the pyramid?

Top of pyramid is square

A cube is a prism with six square faces. Other prisms and pyramids are named for the shape of their bases.

Let’s Review Identify characteristics of a cylinder: Bases Lateral surface (face) Edges

Core Lesson Distance from center is constant. Therefore it’s a circle Horizontal Cross-section r r Slices parallel to base are congruent to base

Vertical Cross-section Vertical slice always creates a parallelogram

A Common Misunderstanding A diagonal cross-section creates a circle Circles are only created by horizontal cross-sections

Core Lesson Distance from center is not constant Actually an ellipse Diagonal Cross-section b a

Ice cream factories test how consistently the ingredients are distributed through each carton by cutting cartons in half for a good view. Describe the 2D figure that result from slicing a carton vertically through the top.

Core Lesson Ice cream factories test how consistently the ingredients are distributed through each carton by cutting cartons in half for a good view. Describe the 2D figures that result from slicing a carton vertically through the top. Vertical: rectangle

Let’s Review Identify characteristics of a cone: Base Lateral surface (face) Edge Vertex

Core Lesson Intersecting curved lateral surface Horizontal Cross-section Geometrically similar to base: circle

A Common Misunderstanding A diagonal cross-section creates a circle Circles are only created by horizontal cross-sections

Core Lesson Distance from center is not constant Actually an ellipse Diagonal Cross-section b a

Core Lesson Interactive

In this lesson, you will learn how to predict the 3D results of rotating simple figures by analyzing the effects of rotations.

How do you predict the 3D result of rotating a 2D figure? What 3D shape would result from rotating this rectangle?

Core Lesson Edges perpendicular to axis draw flat faces Rectangle: Axis Bisecting Edges parallel to axis draw curved surfaces Rotation creates: cylinder

Edges perpendicular to axis draw flat faces Rectangle: Axis Along Edge Edges parallel to axis draw curved surfaces Rotation creates: cylinder

Axis bisects triangle Rotating Triangle in 3D Rotation creates a cone

Curved edges draw curved surfaces Circle: Axis Bisecting Rotation creates: sphere

The End !!!