# Ch 17: CAHSEE - Triangles, the Pythagorean Theorem & Congruency: Tutoring Solution

### About This Chapter

## How it works:

- Begin your CAHSEE math exam prep.
- Identify the triangle concepts that you're stuck on.
- Find fun videos on the topics you need to understand.
- Press play, watch and learn!
- Complete the quizzes to test your understanding.
- As needed, submit a question to one of our instructors for personalized support.

## Who's it for?

This chapter of our CAHSEE Tutoring Solution will benefit any student who is trying to learn about triangles, the Pythagorean theorem and congruency and earn passing scores on the exam. This resource can help students including those who:

- Struggle with understanding isosceles and right triangles, angles, congruency postulates or any other triangles topic
- Have limited time for studying
- Want a cost effective way to supplement their math learning
- Prefer learning about math visually
- Find themselves struggling with their CAHSEE math exam preparation
- Cope with ADD or ADHD
- Want to get ahead in high school math
- Don't have access to CAHSEE math exam study materials

## Why it works:

**Engaging Tutors:**We make learning about triangles, the Pythagorean theorem and congruency simple and fun.**Cost Efficient:**For less than 20% of the cost of a private tutor, you'll have unlimited access 24/7.**Consistent High Quality:**Unlike a live math tutor, these video lessons are thoroughly reviewed.**Convenient:**Imagine a tutor as portable as your laptop, tablet or smartphone. Learn about triangles, the Pythagorean theorem and congruency on the go!**Learn at Your Pace:**You can pause and rewatch lessons as often as you'd like, until you master the material.

## Learning Objectives

- Learn the applications of the Pythagorean theorem.
- Identify similar triangles.
- Understand the applications of similar triangles.
- Classify triangles according to their angles and sides.
- Solve problems involving triangles and their angles.
- Define congruency.
- Become familiar with the triangle congruence postulates.
- Be able to prove the congruency of isosceles triangles.
- Understand the LA and LL theorems.

### 1. The Pythagorean Theorem: Practice and Application

The Pythagorean theorem is one of the most famous geometric theorems. Written by the Greek mathematician Pythagoras, this theorem makes it possible to find a missing side length of a right triangle. Learn more about the famous theorem here and test your understanding with a quiz.

### 2. 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.

### 3. Applications of Similar Triangles

Similar triangles are used to solve problems in everyday situations. Learn how to solve with similar triangles here, and then test your understanding with a quiz.

### 4. Classifying Triangles by Angles and Sides

Not all triangles are the same. There are equilateral, isosceles and scalene triangles. Then there are right, acute and obtuse triangles. In this lesson, we'll learn how to classify triangles using their sides and angles.

### 5. 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.

### 6. 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.

### 7. Congruency of Isosceles Triangles: Proving the Theorem

Isosceles triangles have two equal sides. Are the base angles also equal? In this lesson, we'll prove how this is true. We'll also prove the theorem's converse.

### 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. Alternate Exterior Angles: Definition & Theorem

In this lesson, learn why the concept of alternate exterior angles is so important and so very useful for you when you are working with a pair of parallel lines.

### 10. Alternate Interior Angles: Definition, Theorem & Examples

In this lesson, you will learn how to identify alternate interior angles and how to use the theorem to find missing angles and to solve everyday geometry problems.

### 11. Pentagonal Prism: Definition & Properties

In this lesson, you'll find out what qualities make up a prism and what a pentagonal prism is. You'll also learn the basic properties found in all pentagonal prisms.

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### Other Chapters

Other chapters within the CAHSEE Math Exam: Tutoring Solution course

- CAHSEE - Number Theory & Basic Arithmetic: Tutoring Solution
- CAHSEE - Problems with Decimals and Fractions: Tutoring Solution
- CAHSEE - Problems with Percents: Tutoring Solution
- CAHSEE - Problems with Radical Expressions & Equations: Tutoring Solution
- CAHSEE - Problems with Algebraic Expressions and Equations: Tutoring Solution
- CAHSEE - Algebraic Linear Equations & Inequalities: Tutoring Solution
- CAHSEE - Problems with Exponents: Tutoring Solution
- CAHSEE - Overview of Functions: Tutoring Solution
- CAHSEE - Rational Expressions: Tutoring Solution
- CAHSEE - Calculations with Ratios, Percent & Proportions: Tutoring Solution
- CAHSEE - Matrices and Absolute Value: Tutoring Solution
- CAHSEE - Quadratics & Polynomials: Tutoring Solution
- CAHSEE - Geometry: Graphing Basics: Tutoring Solution
- CAHSEE - Graphing on the Coordinate Plane: Tutoring Solution
- CAHSEE - Measurement in Math: Tutoring Solution
- CAHSEE - Properties of Shapes: Tutoring Solution
- CAHSEE - Perimeter, Area & Volume in Geometry: Tutoring Solution
- CAHSEE - Statistics, Probability & Working with Data: Tutoring Solution
- CAHSEE - Mathematical Reasoning: Tutoring Solution
- CAHSEE - Logic: Tutoring Solution