# 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

Triangle congruence postulates of side-side-side (SSS), side-angle side (SAS), or angle-side-angle (ASA) refer to truths about triangles without the need for proof. Explore the SSS, SAS, and ASA triangle congruence postulates in detail and learn how to apply them with provided examples.

### 2. Congruence Proofs: Corresponding Parts of Congruent Triangles

A congruent proof applied to triangles can be summed in the theorem that states that ~'corresponding parts of congruent triangles are congruent~' (CPCTC). See this concept in action through three practice problems demonstrating its validity.

### 3. Converse of a Statement: Explanation and Example

A converse statement is formed by interchanging the hypothesis and conclusion in a conditional statement. Learn about conditional statements and examples and explanations of converse statements.

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

Proving the relationship of figures through congruence uses properties of sides and angles. On the other hand, similarity can be used to prove a relationship through angles and sides of the figure. Learn more of these properties through the examples provided.

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

The AAS Theorem asserts that when two angles and any given side are congruent between two triangles, the triangles are congruent. Explore this concept through practicing an example problem, and demonstrate the proof to find congruence.

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

The hypotenuse angle or HA theorem states that if a hypotenuse and acute angle of a right triangle is identical to the angles of another right triangle, the two are congruent. Use a series of examples to learn how to prove, explain, and practice the HA theorem.

### 7. The HL (Hypotenuse Leg) Theorem: Definition, Proof, & Examples

The hypotenuse leg (HL) theorem states that two right triangles are congruent if the hypotenuse & one leg of a right triangle are congruent to the hypotenuse/leg of another right triangle. Learn about the definition, proof of the HL theorem through examples.

### 8. Perpendicular Bisector Theorem: Proof and Example

The perpendicular bisector theorem asserts that the point of perpendicular bisection of a segment is equidistant from either end. Examine the proofs, and the converse of this theorem through the provided examples.

### 9. Angle Bisector Theorem: Proof and Example

An angle bisector is a line that bisects the angle it's drawn from. Study the definition of angle bisector theorem, how to prove it, and examples of this theorem.

### 10. Congruency of Right Triangles: Definition of LA and LL Theorems

Two theorems useful to proving whether right triangles are congruent are the leg-acute (LA), and leg-leg (LL) theorems. Learn about the features of right triangles and how to use the LA and LL theorems to establish congruence between two right triangles.

### 11. Congruency of Isosceles Triangles: Proving the Theorem

The congruency of isosceles triangles is based on the theorem that states if two sides of the triangle are congruent, the opposite angles of these sides are also congruent. Learn how to prove the theorem of congruency of isosceles triangles and also how to prove the converse of the theorem.

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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