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 GACE Mathematics (522): Practice & Study Guide
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Ch 35: GACE Math: Triangles, Theorems & Proofs

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About This Chapter

As you prepare for the GACE Mathematics exam, review the material of this chapter to reinforce what you know about proving the triangles. With focused study, you'll fortify your understanding of the parts, properties, and theorems used to solve problems with triangles.

GACE Math: Triangles, Theorems & Proofs - Chapter Summary

Use this chapter to improve your ability to work geometrical problems involving triangles as part of your preparation for the Georgia Assessments for the Certification of Educators (GACE) in Mathematics. In these lesson videos, our professional instructors will guide you through a series of examples and problems with triangles, demonstrating the use of theorems and proofs. Our instructors will help you prepare for test items on:

  • Triangle congruence postulates and congruence proofs
  • Finding and assessing the converse of a statement
  • Angle-Angle-Side, Hypotenuse Angle, and the Hypotenuse Leg Theorem
  • Perpendicular bisector theorem and angle bisector theorem
  • Right triangles and the LA and LL theorems
  • Congruency of isosceles triangles

Take a look at each of the videos in the order that you prefer. The chapter is completely self-paced, so you can re-watch the lessons until you fully understand their concepts. You may take the follow-up quizzes to test your retention.

GACE Math: Triangles, Theorems & Proofs Objectives

GACE Mathematics is used in the state of Georgia to measure educators' mathematical abilities. This computer-based certification exam is made up of two subtests that can be taken together or at separate times. There are 45 multiple-choice questions on each of the the GACE Mathematics Tests, and they both have a two-hour time limit. The Geometry subarea of Test II contains about 30% of the subtest's questions, and some may focus on triangles, theorems and proofs. This chapter has been compiled to help you improve your knowledge of these areas so that you will be prepared for them on test day.

11 Lessons in Chapter 35: GACE Math: Triangles, Theorems & Proofs
Chapter Practice Test
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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
Chapter Practice Exam
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Practice Final Exam
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