About This Chapter
Relationships Between Figures in Geometry - Chapter Summary
This chapter will help you review relationships between figures in geometry. You'll be able to study shapes, proofs and ratios with these video lessons and quizzes. Our lessons include easy to understand definitions and examples of these mathematical concepts. You can access this chapter if you're interested in studying:
- 2D and 3D shapes
- Lateral area, surface area and total surface area
- Congruency proofs and the congruency of right triangles
- Congruence postulates
- Trigonometric ratios and identities
The video lessons include timelines that allow you to go directly to the information you'd like to review. You'll also have access to transcripts of the lessons, if you're more comfortable reviewing the steps in mathematical processes that way.
1. What are 2D Shapes? - Definition & Examples
In this lesson, you will find out how a flat piece of paper will help you determine what shapes are considered 2D. You will also learn the wide variety of 2D shapes you may encounter in life.
2. What are 3D Shapes? - Definition & Examples
What's the difference between 2D and 3D shapes? Learn the answer to this question in this lesson. You will also explore what makes spheres and cubes 3D shapes.
3. Lateral Area: Definition, Formula & Examples
Lateral surface area is finding the area of the sides of a three-dimensional geometric figure. The formulas for lateral surface area are based on the base of the figure and whether the figure is a prism, cone, or pyramid. We will investigate all of these.
4. What is Surface Area? - Definition & Formulas
In this lesson, you use general and specific formulas to learn how to find the surface area of three-dimensional shapes, such as cubes, prisms, spheres, cones and cylinders.
5. Total Surface Area: Definition & Formula
This lesson will define and explain what total surface area is and provide the formulas for calculating total surface area, as well as an explanation about why they work.
6. Congruence Proofs: Corresponding Parts of Congruent Triangles
Congruent triangles have congruent sides and angles, and the sides and angles of one triangle correspond to their twins in the other. In this lesson, we'll try practice with some geometric proofs based around this theorem.
7. Triangle Congruence Postulates: SAS, ASA & SSS
When we have two triangles, how can we tell if they're congruent? They may look the same, but you can be certain by using one of several triangle congruence postulates, such as SSS, SAS or ASA.
8. Congruency of Right Triangles: Definition of LA and LL Theorems
In this lesson, we'll learn two theorems that help us prove when two right triangles are congruent to one another. The LA theorem, or leg-acute, and LL theorem, or leg-leg, are useful shortcuts for proving congruence.
9. Trigonometric Ratios and Similarity
Where do terms like sine, cosine and tangent come from? In this lesson, we'll learn about how similarity with right triangles leads to trigonometric ratios.
10. Trigonometric Identities: Definition & Uses
After watching this video lesson, you will understand what a trigonometric identity is. You will also know the different kinds of identities you will come across.
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