About This Chapter
Triangles, the Pythagorean Theorem & Congruency - Chapter Summary
Get ready for the CAHSEE math section with this chapter's video lessons. Instructors can introduce you to the properties of triangles, the Pythagorean theorem and the postulates used to prove congruence. There are also practice problems designed to help you:
- Identify similar triangles
- Classify triangles by angles and sides
- Determine congruence of right and isosceles triangles
Video lessons and transcripts define vocabulary terms, explain key concepts and introduce mathematical formulas. You can even try your hand at solving equations with the corresponding self-assessment quizzes. Use these resources to find out what's on the exam, create a study plan and familiarize yourself with how test questions are formatted.
Triangles, the Pythagorean Theorem & Congruency - Objectives
If you're a California high school student, scores on the CAHSEE math section will be used to determine your proficiency in this subject area and your eligibility for a high school diploma.
Video lessons and quizzes in this chapter can help you tackle the exam's Measurement and Geometry section, which includes 17 out of 80 total multiple-choice questions. You'll need to know when to use the Pythagorean theorem and how to determine the length of a triangle's side when given measurements for the other two. Questions on this part of the test also ask you to determine the congruence of shapes and solve word problems.
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. What Are Congruent Figures? - Definition & Examples
In this lesson, you'll learn what congruent figures are. You'll also see a few examples of congruent and non-congruent figures. Then, test your knowledge with a brief quiz.
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 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.
9. 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.
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Other chapters within the CAHSEE Math Exam: Test Prep & Study Guide course
- Number Theory & Basic Arithmetic
- Problems with Decimals and Fractions
- Problems with Percents
- Problems with Radical Expressions & Equations
- Problems with Algebraic Expressions and Equations
- Algebraic Linear Equations & Inequalities
- Problems with Exponents
- Overview of Functions
- Rational Expressions & Practice
- Calculations with Ratios, Percent & Proportions
- Understanding Matrices & Absolute Value
- Quadratics & Polynomials
- Geometry: Graphing Basics
- Graphing on the Coordinate Plane
- Measurement in Math
- Properties of Shapes
- Perimeter, Area & Volume in Geometry
- Statistics, Probability & Working with Data
- Mathematical Reasoning
- Basic Mathematical Logic
- CAHSEE Math Exam Flashcards