# Ch 17: HiSET Mathematics: Triangle Theorems and Proofs

### About This Chapter

## HiSET Mathematics: Triangle Theorems and Proofs - Chapter Summary

For those looking to pass the HiSET math exam, you have come to the right place. Our short video lessons cover the material you will need to know in funny, practical ways that will keep you enjoying your exam preparation. Subject-matter experts lead you through each lesson, and our transcripts reinforce key terms that are on the exam, including:

- Triangle congruence
- Corresponding parts of congruent triangles
- Converse of a statement and similarity
- Angle-angle-side theorem
- Hypotenuse angle and hypotenuse leg theorems
- Perpendicular bisector and angle bisector theorems
- Congruency of right and isosceles triangles

Depending on your mathematical strengths, you can watch each of the videos from beginning to end, or you can focus only on certain concepts by using the video tags. Taking the included quizzes will allow you to evaluate your retention.

### Objectives of the HiSET Mathematics: Triangle Theorems and Proofs Chapter

The HiSET math exam will assess your understanding of key triangle theorems and proofs. The topics in this chapter are in the Measurement/Geometry part of the exam, which constitutes 18% of the entire math test.

All of the questions are multiple-choice, leading you to choose one correct answer from a list of possibilities. Our lesson quizzes at the end of each lesson can help you gauge your comprehension of the material as well as give you the opportunity to practice solving multiple-choice problems.

### 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.

### 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.

### 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.

### 4. How to Prove Relationships in Figures using Congruence & Similarity

In this lesson, we'll look at similar and congruent figures and the properties that they hold. We will then look at how to use these properties to prove relationships in these figures in various 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.

### 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.

### 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.

### 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.

### 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.

### 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.

### 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.

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### Other Chapters

Other chapters within the HiSET Mathematics: Prep and Practice course

- HiSET Mathematics: Mathematical Reasoning
- HiSET Mathematics: Properties of Real Numbers
- HiSET Mathematics: Fractions
- HiSET Mathematics: Decimals and Percents
- HiSET Mathematics: Ratios and Proportions
- HiSET Mathematics: Vector Operations
- HiSET Mathematics: Matrices and Determinants
- HiSET Mathematics: Exponents and Exponential Expressions
- HiSET Mathematics: Absolute Value Problems
- HiSET Mathematics: Rational Expressions
- HiSET Mathematics: Radical Expressions
- HiSET Mathematics: Imaginary and Complex Numbers
- HiSET Mathematics: Measurements and Conversions
- HiSET Mathematics: Foundations of Geometry
- HiSET Mathematics: Introduction to Geometric Figures
- HiSET Mathematics: Properties of Triangles
- HiSET Mathematics: Parallel Lines and Polygons
- HiSET Mathematics: Quadrilaterals
- HiSET Mathematics: Circular Arcs and Circles
- HiSET Mathematics: Geometric Solids
- HiSET Mathematics: Summarizing Data
- HiSET Mathematics: Probability
- HiSET Mathematics: Probability Distributions
- HiSET Mathematics: Sampling
- HiSET Mathematics: Regression and Correlation
- HiSET Mathematics: Algebraic Expressions
- HiSET Mathematics: Linear Equations
- HiSET Mathematics: Inequalities
- HiSET Mathematics: Quadratic Equations
- HiSET Mathematics: Polynomials
- HiSET Mathematics: Functions
- HiSET Mathematics Flashcards