Name Date

Geometry Period Lesson 13-1

Lesson 13-1: Solid Figures Formed by Translations

Leanning goal: How are solid figures formed through translations, and what are the properties of these solids?

Class Discussion:

Imagine this! You stand inside a hula hoop, which is dipped in bubble solution. Lift the hula hoop straight up. Can you sketch the shape that the bubble will take? Do you know what this is called? What objects do you know that take this shape?

Think-Pair-Share

What type of transformation is shown here?

What are the important aspects/ properties of this transformation?

Make connections! How does this relate to the class discussion?

Google Sketch Up!Thinking in 3-D...Circles

Sketch the figure formed when a circle is "pushed" into 3 dimensions.

Vocab Alert! Important Terms Below! What does the resulting solid look like?

Base: Base View:

Lateral Face: Lateral View:

All about Cylinders!

A cylinder is...

A 3-D Object. Two circular bases that are ____________ and ______________. Lateral faces are ______________. Can be formed when a circle is translated or “Pushed” into 3-D.

Other Important Properties:

Like a prism, but the bases are NOT polygons.

Cross Sections The 2D shape that appears when you cut/slice a 3D solid with a plane:

Two Types!

Parallel to the base (same shape as base view)

Perpendicular to the base ( same shape as lateral view)

Back to Google Sketch Up!Thinking in 3-D... Polygons

Let’s sketch some other shapes we could push into 3D!

What does the resulting solid look like?

BASE VIEW (cross Sect. ∥ to base) Lateral View( Cross sect. ⊥ to the base)

All about Prisms

A prism is...

A 3D solid Formed by translating a polygon. Two polygonal bases that are ____________ and _____________.

Other Important Properties

Prisms are names by their _________________. Lateral faces are always ___________________ except for the ________. All their faces are ______. Lateral Edges (the lines formed when the faces meet) are always ___________ and ____________. The number of lateral faces corresponds to the number of ___________ the base has.

Back to Google Sketch Up!Thinking in 3-D...Sketch the figure formed when the area of the square is "pulled" into 3 dimensions:

As a class!

When we "pushed" a square into 3-D, we were using the concept of translations from our transformations unit.

Cross sections!

What is the cross section parallel to the base?

What is the cross section perpendicular to the base?

What does the resulting solid look like?

BASE VIEW (cross Sect. ∥ to base) Lateral View( Cross sect. ⊥ to the base)

What transformation(s) do you think are required to create the solid below from the "pre-image" of the square base?

All about Pyramids

A pyramid is... A 3D solid Formed by a ____________and a ___________.

Other Important Properties: One base that is a polygon. Named by the base polygon. Lateral edges are congruent. Lateral faces are Isosceles triangles.

Name Date

Integrated Geometry Period 13-1 Practice

Applying our Knowledge1. Name each of the solids below. Draw the base and lateral views and name the cross sections.

Base View:

What 2D shape is the cross section parallel to the base?

Base View:

What 2D shape is the cross section parallel to the base?

Base View:

What 2D shape is the cross section parallel to the base?

Lateral View:

What 2D shape is the cross section that is perpendicular to the base?

Lateral View:

What 2D shape is the cross section that is perpendicular to the base?

Lateral View:

What 2D shape is the cross section that is perpendicular to the base?

2. What appears to be a square piece of fabric is laid out on the ground and the corners are hammered in place. A pole is placed under the fabric and used to raise a shelter. What is the base view? What is the lateral view?

3a) A redwood tree grows for 400 years before it is tragically cut down to make paper. For transportation, the tree is sliced. What are the possible shapes the tree could take?

3b) Once the tree has been processed into paper, your geometry teacher uses it to make her copies for class. She stacks all her copies in a single pile. What solids could be formed by the copies?

5.

6.

7) For the following, sketch and name the solid that will match with the given cross section.