Ch 29: FTCE Middle Grades Math: Right Triangle Proofs

About This Chapter

In this chapter, you will review the theorems and proofs of right triangles, as well as the properties of right triangles and special right triangles as you prepare for the FTCE Middle Grades Mathematics exam.

FTCE Middle Grades Math: Right Triangle Proofs - Chapter Summary

Use these videos to prepare for questions on the Florida Teacher Certification Examinations (FTCE) Middle Grades Mathematics 5-9 exam that may involve the use of right-triangle proofs and theorems. In these lessons, our professional instructors will use example problems to explain:

  • The hypotenuse-angle theorem and the hypotenuse-leg theorem
  • Uses of the leg-acute-angle theorem and leg-leg theorem
  • Properties of right triangles and how they can be used to solve problems
  • Special properties of 30-60-90 and 45-45-90 right triangles
  • The Pythagorean theorem and its uses

To reinforce your retention of the information presented in these lessons, read the lesson transcripts. Then, test your understanding of the material by completing the lesson quizzes. Review your quiz results to discover topics you don't understand, and then use the video tags to return to and study the parts of the lessons that discussed those topics.

10 Lessons in Chapter 29: FTCE Middle Grades Math: Right Triangle Proofs
Test your knowledge with a 30-question chapter practice test
The HA (Hypotenuse Angle) Theorem: Proof, Explanation, & Examples

1. The HA (Hypotenuse Angle) Theorem: Proof, Explanation, & Examples

In this lesson, we'll learn about the hypotenuse angle theorem. With this theorem, we can prove two right triangles are congruent with just congruent hypotenuses and acute angles.

The HL (Hypotenuse Leg) Theorem: Definition, Proof, & Examples

2. The HL (Hypotenuse Leg) Theorem: Definition, Proof, & Examples

In this lesson, we'll learn about the hypotenuse leg theorem. This theorem enables us to prove two right triangles are congruent based on just two sides.

Congruency of Right Triangles: Definition of LA and LL Theorems

3. 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.

Properties of Right Triangles: Theorems & Proofs

4. Properties of Right Triangles: Theorems & Proofs

In this lesson, you will learn about the properties of and theorems associated with right triangles, which have a wide range of applications in math and science. Specifically, we will discuss and prove the Pythagorean theorem and the right triangle altitude theorem. Let's get started.

Special Right Triangles: Types and Properties

5. Special Right Triangles: Types and Properties

Not all right triangles are the same. In this lesson, we'll look at two special right triangles (30-60-90 and 45-45-90) that have unique properties to help you quickly and easily solve certain triangle problems.

Pythagorean Theorem: Definition & Example

6. 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.

The Pythagorean Theorem: Converse and Special Cases

7. 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.

Finding Distance with the Pythagorean Theorem

8. Finding Distance with the Pythagorean Theorem

How much faster is it to cut the corners in a race around the block? In this lesson, review the Pythagorean Theorem, and figure out how to solve without a right triangle.

Solving Right Triangles Using Trigonometry & the Pythagorean Theorem

9. Solving Right Triangles Using Trigonometry & the Pythagorean Theorem

The Pythagorean Theorem is one of the most well-known and useful math equations. Its simple form and abundant uses make it one of the most helpful processes to learn in math. In this lesson, learn how to solve right triangles using the Pythagorean Theorem.

Solving Right Triangles Using Inverse Trigonometric Ratios

10. Solving Right Triangles Using Inverse Trigonometric Ratios

Solving a right triangle means finding all the sides and all the angles. In this lesson you will see when and how to use inverse trigonometric functions for determining unknown angles.

Chapter Practice Exam
Test your knowledge of this chapter with a 30 question practice chapter exam.
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Practice Final Exam
Test your knowledge of the entire course with a 50 question practice final exam.
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Other Chapters

Other chapters within the FTCE Middle Grades Mathematics 5-9 (025): Practice & Study Guide course

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