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Ch 36: OAE Mathematics: Triangle Theorems & Proofs

About This Chapter

Trying to remember triangle theorems for the OAE Mathematics test? Examine the video lessons in this chapter and let us help you remember the finer points of all the different theorems and proofs for triangles.

OAE Mathematics: Triangle Theorems & Proofs - Chapter Summary

Delve into this chapter as you go through the steps for determining the different measurements of triangles. The OAE Mathematics test includes a fair amount of geometry questions, and some of those questions could address the following topics:

  • Congruence proofs
  • HA, AAS, and HL theorems
  • Similarity and congruence relationships
  • The congruency of different types of triangles
  • The congruence postulates of triangles
  • Perpendicular bisector and angle bisector theorems

Use our video lessons as a way to bridge the gap between what you know and what you don't know very well. You can view the lessons at home or on any device that connects to the Internet. Make studying for the OAE Mathematics test work for you and your schedule by reviewing our short video lessons whenever and wherever you can.

OAE Mathematics: Triangle Theorems & Proofs Chapter Objectives

Mathematics educators in Ohio may need to take the OAE Mathematics test in order to obtain a license for employment. This comprehensive test examines your knowledge of five key mathematical categories. The questions are in a multiple-choice format, and you will have around four hours to answer 150 questions. This particular chapter addresses a topic found within the measurement and geometry section; about 19% of your final test score comes from questions in this section.

11 Lessons in Chapter 36: OAE Mathematics: 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

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Other Chapters

Other chapters within the Ohio Assessments for Educators - Mathematics (027): Practice & Study Guide course

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