# Ch 24: HSPT Test: Triangle Theorems & Proofs

### About This Chapter

## HSPT Test: Triangle Theorems & Proofs - Chapter Summary

In these lessons, you can review the angle relationships that form triangles and the reasoning behind them. Use the lessons to prepare for HSPT test questions about the following:

- Applications of similar triangles
- Congruence postulates and proofs
- Using congruence and similarity to prove relationships
- Definition and explanation of the converse of a statement
- HA, AAS and HL theorems
- Perpendicular and angle bisector theorems
- Right and isosceles triangle congruency

To make referral and identification easy, our transcripts highlight key vocabulary for you. And there are links to help you move freely back and forth between the lesson quizzes and the videos. This makes reviewing the material quick and convenient, and the dashboard helps you stay organized and on track.

### HSPT Test: Triangle Theorems & Proofs Chapter Objectives

The HSPT test is part of the admissions, screening, placement and scholarship process for students applying to select Catholic high schools, and it is given in the eighth grade. The test measures reading, math, language, quantitative and verbal skills. The lessons in this chapter align with the skills measured in the mathematics section. This part of the test contains 64 questions out of the 298 that comprise the overall test.

This is a multiple-choice test, requiring you to choose one correct answer from perhaps four or five possible responses. The test is given on paper.

### 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.

### 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.

### 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.

### 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.

### 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.

### 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.

### 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.

### 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.

### 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.

### 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.

### 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.

### 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.

### 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.

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### Other Chapters

Other chapters within the HSPT Test: Practice & Study Guide course

- HSPT Test: Quantitative Reasoning
- HSPT Test: Mathematical Sequences & Series
- HSPT Test: Understanding Real Numbers
- HSPT Test: Operations in Math
- HSPT Test: Understanding Integers
- HSPT Test: Irrational & Rational Numbers
- HSPT Test: Solving & Graphing Inequalities
- HSPT Test: Using Estimation in Mathematics
- HSPT Test: Using Decimals
- HSPT Test: Understanding Fractions
- HSPT Test: Using Percents
- HSPT Test: Ratios & Proportion
- HSPT Test: Square Roots
- HSPT Test: Exponents & Exponential Expressions
- HSPT Test: Scientific Notation
- HSPT Test: Standard Measurement
- HSPT Test: Introduction to Geometry
- HSPT Test: Perimeter, Area & Volume
- HSPT Test: Symmetry, Similarity & Congruence
- HSPT Test: Properties of Lines
- HSPT Test: Plotting Graphs
- HSPT Test: Transformations
- HSPT Test: Triangle Basics
- HSPT Test: The Pythagorean Theorem
- HSPT Test: Graphing Data
- HSPT Test: Data Analysis
- HSPT Test: Probability & Permutations
- HSPT Test: Properties of Functions
- HSPT Test: Graphing Functions
- HSPT Test: Factoring in Algebra
- HSPT Test: Basic Algebraic Expressions
- HSPT Test: Algebraic Distribution
- HSPT Test: Solving Rational Expressions
- HSPT Test: Linear Equations
- HSPT Test: Systems of Linear Equations
- HSPT Test: Mathematical Reasoning
- HSPT Test: Verbal Reasoning
- HSPT Test: Basics of Grammar
- HSPT Test: Spelling & Punctuation
- HSPT Test: Syntax & Sentence Structure
- HSPT Test: Interpreting Readings
- HSPT Test: Reading Comprehension
- HSPT Test: Understanding Meaning in Reading
- HSPT Test Flashcards