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Ch 55: MTTC Math (Secondary): Triangle Theorems & Proofs

About This Chapter

Develop mastery of triangles, theorems and proofs in order to answer relevant questions on the MTTC Math (Secondary) examination. Taking your prior studies into account, the online video lessons in this chapter can be used as part if your a review process.

MTTC Math (Secondary): Triangle Theorems and Proofs - Chapter Summary

This chapter presents you with information about triangles, theorems and proofs. Add to your knowledge in these areas before you sit for the MTTC Math (Secondary) examination. Re-discover methods for measuring a triangle's sides and for determining whether triangles are congruent. The video lessons include key definitions and practice opportunities. Exploring the concepts in this chapter could help you with:

  • Explaining how to use and solve with similar triangles
  • Using congruence postulates
  • Understanding geometric congruence proofs
  • Explaining the converse of a statement
  • Providing examples of the AAS, HA and HL theorems
  • Using congruence and similarity to prove relationships
  • Proving the congruency of right and isosceles triangles
  • Describing similarity transformations
  • Proving the perpendicular and angle bisector theorems
  • Identifying the properties of right triangles

Educated mathematics instructors make an effort to expand your understanding of triangles, theorems and proofs through this chapter's engaging videos. Ask questions and study interactively at your own pace. The lessons include video tags for moving from topic to topic as well as text transcripts. Self-assessment quizzes could determine your readiness for the MTTC Math (Secondary) examination's questions on triangles, theorems and proofs.

MTTC Math (Secondary): Triangle Theorems and Proofs Objectives

Use your knowledge of triangles, theorems and proofs when you answer questions in the 'Measurement and Geometry' subarea of the four-part MTTC Math (Secondary) examination. This subarea is equal to 22% of the entire examination and score.

You must correctly answer 80 multiple-choice questions as you pursue a mathematics teaching certification in Michigan. There are paper and computer versions of the examination. If you take the paper-based examination, you must finish in under four hours and 30 minutes. The time limit for the computer-administered version is two hours and 30 minutes.

14 Lessons in Chapter 55: MTTC Math (Secondary): Triangle Theorems & Proofs
Test your knowledge with a 30-question chapter practice test
Applications of Similar Triangles

1. 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.

Triangle Congruence Postulates: SAS, ASA & SSS

2. 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

3. 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

4. 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.

Similarity Transformations in Corresponding Figures

5. Similarity Transformations in Corresponding Figures

Watch this video lesson to learn how you can tell if two figures are similar by using similarity transformations. Learn how to find the corresponding sides and angles and then how to compare them.

Practice Proving Relationships using Congruence & Similarity

6. 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

7. 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

8. 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

9. 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

10. 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

11. 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

12. 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

13. 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.

Properties of Right Triangles: Theorems & Proofs

14. 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.

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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