# Ch 5: Plane Geometry

### About This Chapter

## Plane Geometry - Chapter Summary

This engaging chapter covers plane geometry and its related subjects, including the notation and symbols used in plane geometry. Our professionally designed lessons explain the different types of triangles and their properties, as well as the properties of quadrilaterals, parallelograms, polygons and trapezoids. You'll also study the definition of the triangle sum theorem, the exterior angle theorem and triangle congruence postulates. Other topics include the definition of the Pythagorean theorem and its converse. This chapter is designed to help you:

- Explain the formula used for the exterior angle theorem
- Measure and find the sum of the angles of a polygon
- Understand congruence as it applies to geometric shapes
- Identify similar triangles
- Compare perpendicular, parallel and transverse lines
- Differentiate between the area formulas for trapezoids, triangles and parallelograms
- Describe the format for geometric proofs

Feel free to access these learning tools on any mobile device or computer 24 hours a day. It's easy to skip ahead or go back to any section of a video lesson using the video tabs feature. If you prefer to study offline, the printable lesson transcripts highlight key concepts and terms. Our instructors are available to offer their assistance if you need it.

### 1. Notation & Symbols in Plane Geometry

This lesson will provide instruction for how to identify and draw the standard notation for points, lines, and angles, as well as symbols for geometric concepts such as measure, length, parallel, perpendicular, congruent, and similar.

### 2. Types of Triangles & Their Properties

This lesson introduces different types of triangles. We'll discuss some different characteristics that are common to all triangles and some properties that are unique to certain types of triangles.

### 3. What is a Quadrilateral? - Definition, Properties, Types & Examples

This lesson explains the definition and properties of a quadrilateral. We will look at examples of two categories of quadrilaterals. At the end, you will be able to test your knowledge with a quiz.

### 4. Properties of Shapes: Quadrilaterals, Parallelograms, Trapezoids, Polygons

Four-sided objects are more than just squares and rectangles. In this lesson, we'll discuss quadrilaterals, parallelograms and trapezoids. We'll also discuss polygons, objects that can have more sides than you can count.

### 5. Triangle Sum Theorem: Definition & Examples

In this lesson, we will learn about the Triangle Sum Theorem. We will also look at how useful the Triangle Sum Theorem is when looking for missing angle measurements inside of a triangle.

### 6. Exterior Angle Theorem: Definition & Formula

While it may sound scary at first, the exterior angle theorem is a simple formula that helps us solve for the missing angle of a triangle. Rather than examining a formal proof of the theorem, we'll focus on the formula itself and how it can be applied.

### 7. How to Measure the Angles of a Polygon & Find the Sum

Watch this video lesson to learn the one formula that lets you find the measure of angles in any regular polygon. Also, learn how you can tell if you are working with a regular polygon or not.

### 8. Congruence in Geometric Shapes

Watch this video lesson to learn how you can determine whether two shapes are congruent or not. You will learn what the one criterion is when determining congruency between two shapes.

### 9. 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.

### 10. How to Identify Similar Triangles

Similar triangles have the same characteristics as similar figures but can be identified much more easily. Learn the shortcuts for identifying similar triangles here and test your ability with a quiz.

### 11. 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.

### 12. Pythagorean Theorem: Definition & Example

Learn what the Pythagorean Theorem says about a right triangle and the relationships of its three sides to each other by watching this video lesson. Also learn how you can use this to your advantage when solving problems.

### 13. The Pythagorean Theorem: Converse and Special Cases

The Pythagorean Theorem is a famous theorem for right triangles. Watch this video to learn how the Pythagorean Theorem relates to the law of cosines and how the converse of the Pythagorean Theorem can help you identify right triangles.

### 14. How Area Formulas of Triangles, Parallelograms & Trapezoids Relate

Triangles, parallelograms, and trapezoids are all two-dimensional shapes that show up in the world around us. In this lesson, we'll look at the areas of these shapes and how they relate to each other.

### 15. Geometric Proofs: Definition and Format

Do you have something to prove? Can you explain why? In this lesson, we'll learn all about geometric proofs, including the parts that comprise a proof.

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### Other Chapters

Other chapters within the HSC Mathematics: Exam Prep & Syllabus course

- Mathematical Proofs & Reasoning
- Basic Arithmetic & Algebra
- Factorization of Binomials & Trinomials
- Types of Equations & Inequalities
- Circle Plane Geometry
- Probability & Randomization
- Arithmetic & Geometric Series
- Trigonometric Ratios
- Geometrical Representations of Functions
- Linear Functions & Lines
- Derivatives of Functions
- Quadratic Polynomials & Parabolas
- Geometrical Applications of Differentiation
- Integration
- Logarithmic & Exponential Functions
- Calculating Trigonometric Functions
- Understanding Inverse Functions
- Factoring & Graphing Polynomials
- Roots & Coefficients of Polynomials
- Binomial Theorem & Probability
- Graphing & Solving Functions
- Solving & Graphing Complex Numbers
- Geometric Representations of Complex Numbers
- Square Roots, Powers & Roots of Complex Numbers
- Conic Sections Basics
- The Ellipse in Algebra
- The Hyperbola
- The Rectangular Hyperbola
- Calculus Applications: Rate of Change
- Calculus Applications: Velocity & Acceleration
- Calculus Applications: Projectile & Harmonic Motion
- Calculus Applications: Resisted Motion
- Calculus Applications: Circular Motion
- HSC Mathematics Flashcards