Copyright

Ch 36: ORELA Math: Triangle Theorems & Proofs

About This Chapter

Use these quick, entertaining videos to review triangle theorems and proofs as part of your ORELA Math test preparation. Don't hesitate to let our instructors know if you have any questions about triangle proofs and theorems as they are experts in the field and available at any time.

ORELA Math: Triangle Theorems & Proofs - Chapter Summary

This chapter offers a varied menu of resources designed to help you master the triangle theorems and proofs you have to know to become an ORELA-certified math educator. Fun, short video lessons and companion transcripts cover:

  • The SAS, ASA and SSS postulates
  • Congruence and similarity proofs
  • The AAS, HA, HL, LA and LL theorems
  • Perpendicular bisector and angle bisector theorems
  • Congruency in right and isosceles triangles

Don't forget to make use of the lesson quizzes, which let you practice using the concepts and figure out which areas need additional review. Ask our instructors any questions you have about triangle theorems and proofs. Use all of the chapter resources at your disposal to solidify your knowledge for the actual exam.

Objectives of the ORELA Math: Triangle Theorems & Proofs Chapter

Use this chapter to study triangle theorems and proofs for the geometry and measurement competency area of the ORELA Math exam, which weighs in at 19% of your exam score. Lesson quizzes let you evaluate your mastery of the ideas and introduce you to the ORELA test format.

You will also be tested on four other areas. Math processes and number sense; trig and calculus; and stats, discrete math and probability are each also weighted for 19% of your score. The final 24% is devoted to patterns, algebra and functions. You will have four hours and fifteen minutes to work through all 150 multiple-choice items on the computer-administered exam.

11 Lessons in Chapter 36: ORELA Math: Triangle Theorems & Proofs
Test your knowledge with a 30-question chapter practice test
Triangle Congruence Postulates: SAS, ASA & SSS

1. 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.

Congruence Proofs: Corresponding Parts of Congruent Triangles

2. Congruence Proofs: Corresponding Parts of Congruent Triangles

Congruent triangles have congruent sides and angles, and the sides and angles of one triangle correspond to their twins in the other. In this lesson, we'll try practice with some geometric proofs based around this theorem.

Converse of a Statement: Explanation and Example

3. Converse of a Statement: Explanation and Example

Just because a conditional statement is true, is the converse of the statement always going to be true? In this lesson, we'll learn the truth about the converse of statements.

Practice Proving Relationships using Congruence & Similarity

4. Practice Proving Relationships using Congruence & Similarity

In geometry, if two shapes are similar they have the same shape but different sizes, while two congruent shapes have the same shape and size. In this lesson, you will learn how to prove that shapes are similar or congruent.

The AAS (Angle-Angle-Side) Theorem: Proof and Examples

5. The AAS (Angle-Angle-Side) Theorem: Proof and Examples

When trying to find out if triangles are congruent, it's helpful to have as many tools as possible. In this lesson, we'll add to our congruence toolbox by learning about the AAS theorem, or angle-angle-side.

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

6. 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

7. 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.

Perpendicular Bisector Theorem: Proof and Example

8. Perpendicular Bisector Theorem: Proof and Example

Perpendicular bisectors are multifunctional lines. They're not only perpendicular to the line in question, they also neatly divide it into two equal halves. In this lesson, we'll learn about the perpendicular bisector theorem.

Angle Bisector Theorem: Proof and Example

9. Angle Bisector Theorem: Proof and Example

The angle bisector theorem sounds almost too good to be true. In this lesson, we set out to prove the theorem and then look at a few examples of how it's used.

Congruency of Right Triangles: Definition of LA and LL Theorems

10. 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.

Congruency of Isosceles Triangles: Proving the Theorem

11. 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.

Chapter Practice Exam
Test your knowledge of this chapter with a 30 question practice chapter exam.
Not Taken
Practice Final Exam
Test your knowledge of the entire course with a 50 question practice final exam.
Not Taken

Earning College Credit

Did you know… We have over 200 college courses that prepare you to earn credit by exam that is accepted by over 1,500 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.

To learn more, visit our Earning Credit Page

Transferring credit to the school of your choice

Not sure what college you want to attend yet? Study.com has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you.

Other Chapters

Other chapters within the ORELA Mathematics: Practice & Study Guide course

Support