# Ch 25: Geometry & 3D Shapes

### About This Chapter

## Geometry & 3D Shapes - Chapter Summary

Our helpful chapter outlines geometry and 3D shapes through a series of brief but informative lessons. These lessons cover geometry topics including points and angles in geometry, properties of concurrent lines in triangles and the differences between parallel, transverse and perpendicular lines. You'll also study the types of platonic solids and how the volume of basic shapes is calculated. Once you complete this chapter, you should be ready to:

- Match angles to show that lines are parallel
- Calculate the angle between a line and a plane
- Give an example of a polyhedron
- Use the midpoint formula
- Detail the formulas used in coordinate geometry
- Explain how to calculate the slope of a line
- Discuss the proofs used in analytic geometry
- Complete practice problems using triangles and angles

Because these test and video lessons are mobile friendly and available 24 hours a day, you can work through them whenever you'd like, on any computer, tablet or smartphone. Use the video tabs feature in the Timeline to skip ahead or go back to a specific section of any video. Our printable lesson transcripts and text lessons are a great way to review essential keywords and definitions.

### 1. Points, Lines & Angles in Geometry

After watching this video lesson, you should understand the basic terms that form the foundation of geometry. Learn what a point is, what a line is, what an angle is, and learn about a special type of angle called a right angle.

### 2. Parallel, Perpendicular and Transverse Lines

What are the different types of lines? Where are they visible in the real world and how can you recognize them? Find out here and test your knowledge with a quiz.

### 3. Parallel Lines: How to Prove Lines Are Parallel

Watch this video lesson to learn how you can prove that two lines are parallel just by matching up pairs of angles. Learn which angles to pair up and what to look for.

### 4. Planes and the Polyhedron: Definition and Example

Did you ever wonder what the pyramids in Egypt have to do with math? Watch this video to find out where in math a pyramid comes into play. Also, learn how flat, 2-dimensional shapes also come into play.

### 5. What Are Platonic Solids? - Definition and Types

Watch this video lesson, and you will learn that there are only five platonic solids in the whole world. You will also learn what they look like and see real-life examples.

### 6. How to Calculate the Volumes of Basic Shapes

Squares pegs = square holes. Triangular pegs = triangular holes. But where does a sphere go? In this lesson, review volumes of common shapes while contrasting a sphere and a cylinder - after all, they both go into the circular hole... right?

### 7. How to Use The Midpoint Formula

The formula for the midpoint of a line segment will tell you how to find the middle of any line segment on the x, y plane. Learn about this formula and see how it is used to find the midpoint of a line segment.

### 8. Coordinate Geometry: Definition & Formulas

In this lesson we'll define coordinate geometry and learn about formulas that are commonly used in coordinate geometry. You can then take a brief quiz to see what you learned.

### 9. Calculating the Slope of a Line: Point-Slope Form, Slope-Intercept Form & More

Being able to calculate the slope of a line is a very useful skill to have. Why? Watch this video lesson to find out and learn how to find the slope when working with various equations and various lines.

### 10. Analytic Geometry: Definition & Proofs

This lesson introduces the subject of analytic geometry. You will see the definitions and formulas of important concepts such as distance, midpoint, and slope, as well as a few simple proof examples.

### 11. Properties of Concurrent Lines in a Triangle

Centroids, orthocenters, incenters, circumcenters, oh my! Don't worry though. In this lesson, we master the various terms for concurrent lines in triangles and match them to altitudes, angle bisectors, perpendicular bisectors and medians.

### 12. Angles and Triangles: Practice Problems

Want more practice solving with angle pairs? How about more review for solving angles in triangles? Look no further. Get more practice here, and test your ability with a quiz.

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### Other Chapters

Other chapters within the MHT-CET: Practice & Study Guide course

- Circular Motion & Gravitation
- Understanding Oscillations
- Understanding Rotational Motion
- Equilibrium & Elasticity
- Electric Force & Charge
- Current Electricity
- Using Electricity in Engineering
- Electromagnetic Induction & Magnetism
- Wave Motion
- Understanding Sound Waves
- Light Waves
- Kinetic Theory of Gasses & Radiation
- Atoms, Molecules & Nuclei in Physics
- Surface Tension & Energy
- Matter, Atomic Structure & Chemical Bonding
- D-Block Elements, Halogens, Noble Gases & Alcohols
- Basic Measurement in Chemistry
- Understanding Chemical Solutions
- Chemical Reactions & Kinetics
- Concepts of Organic Chemistry
- Stereochemistry
- Crystallization & Hydrogenation
- Applications of Chemistry in Everyday Life
- Variance, Probability & Distributions
- Overview of Basic Trigonometry
- Function Operations, Limits & Properties
- Exponents & Logarithms
- Linear Systems
- Vectors in Math
- Introduction to Matrices
- Calculation of Derivatives
- Applications of Derivatives in Calculus
- Integrals & Definite Integrals
- Differential Equations & Applications
- Logic & Algebra
- Plant Reproduction & Growth
- Plant Respiration & Photosynthesis
- DNA, Mendelian Genetics & Inheritance
- Introduction to Genetic Engineering
- Characteristics of Birds & Mammals
- Human Anatomy: Neurology and Endocrinology
- Human Anatomy: Cardiology, Nephrology and Immunology
- Reproduction & Contraception
- Human Disease & Diagnostic Technology
- Origins of Life
- Concepts in Pharmacology
- Concepts in Ecology
- MHT-CET Flashcards