# Ch 36: TExES Physics/Math 7-12: Triangle Theorems & Proofs

### About This Chapter

## TExES Physics/Math 7-12: Triangle Theorems & Proofs - Chapter Summary

To prepare you for questions on triangle theorems and proofs which you may see on the TExES Physics/Mathematics 7-12 exam, the professional instructors of this series of lesson videos will lecture over the uses of congruence and similarity, applications of similar triangles and triangle theorems. After this chapter you should be ready to answer question related to:

- Applications of similar triangles
- Triangle congruence postulates and proofs
- Converse of a statement
- Similarity transformations
- Using similarity and congruence to prove relationships in figures
- AAS, HA, HL, LA and LL theorems
- Perpendicular Bisector and Angular Bisector theorems
- Congruency of isosceles triangles

Further improve your knowledge of these topics by completing lesson worksheets and quizzes. Using the quizzes to identify areas of weakness, and improve your understanding of the material you have not mastered using video tags that are linked to key areas of the lesson videos, or lesson transcripts that present the same material but in an alternative written format.

### TExES Physics/Math 7-12: Triangle Theorems & Proofs - Chapter Objectives

The TExES Physics/Mathematics 7-12 is a computer based certification exam administered to future educators of related subjects in the state of Texas. Test takers are asked to complete 120 multiple-choice questions in a five hour testing session. Of these question 16% cover material on patterns and algebra and 10% covers geometry and measurements. In these two domains you will see some questions on slopes of similar triangles, measurements of right triangles and uses of similar triangles. Improve your understanding of the theorems and proofs that are used to answer these questions by completing the activities of this chapter.

### 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. 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.

### 7. 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.

### 8. 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.

### 9. 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.

### 10. 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.

### 11. 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.

### 12. 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.

### 13. 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.

### 14. 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 TExES Physics/Mathematics 7-12 (243): Practice & Study Guide course

- TExES Physics/Math 7-12: Teaching Math & Science
- TExES Physics/Math 7-12: Basic Arithmetic
- TExES Physics/Math 7-12: Real Numbers
- TExES Physics/Math 7-12: Decimals & Fractions
- TExES Physics/Math 7-12: Ratios, Percent & Proportions
- TExES Physics/Math 7-12: Exponents & Exponential Expressions
- TExES Physics/Math 7-12: Algebraic Expressions & Equations
- TExES Physics/Math 7-12: Rational Expressions
- TExES Physics/Math 7-12: Radical Expressions
- TExES Physics/Math 7-12: Complex & Imaginary Numbers
- TExES Physics/Math 7-12: Number Theory
- TExES Physics/Math 7-12: Vector Operations
- TExES Physics/Math 7-12: Sequences & Series
- TExES Physics/Math 7-12: Functions
- TExES Physics/Math 7-12: Graphing & Functions
- TExES Physics/Math 7-12: Linear Equations
- TExES Physics/Math 7-12: Quadratic Equations
- TExES Physics/Math 7-12: Graphing & Factoring Quadratic Equations
- TExES Physics/Math 7-12: Matrices & Determinants
- TExES Physics/Math 7-12: Polynomials
- TExES Physics/Math 7-12: Exponential & Logarithmic Functions
- TExES Physics/Math 7-12: Trigonometry
- TExES Physics/Math 7-12: Continuity in Calculus
- TExES Physics/Math 7-12: Limits in Calculus
- TExES Physics/Math 7-12: Derivatives & Differentiation in Calculus
- TExES Physics/Math 7-12: Foundations of Geometry
- TExES Physics/Math 7-12: Geometry and Measurement
- TExES Physics/Math 7-12: Geometric Figures
- TExES Physics/Math 7-12: Parallel Lines & Polygons
- TExES Physics/Math 7-12: Properties of Triangles
- TExES Physics/Math 7-12: Geometric Solids
- TExES Physics/Math 7-12: Analytical Geometry
- TExES Physics/Math 7-12: Similar Polygons
- TExES Physics/Math 7-12: Conic Sections
- TExES Physics/Math 7-12: Circular Arcs & Circles
- TExES Physics/Math 7-12: Statistics
- TExES Physics/Math 7-12: Probability
- TExES Physics/Math 7-12: Discrete Probability Distributions
- TExES Physics/Math 7-12: Continuous Probability Distributions
- TExES Physics/Math 7-12: Statistical Inference
- TExES Physics/Math 7-12: Mathematical Reasoning
- TExES Physics/Math 7-12: Applied Math
- TExES Physics/Math 7-12: Scientific Inquiry & Process
- TExES Physics/Math 7-12: Vectors & Scalars
- TExES Physics/Math 7-12: Kinematics
- TExES Physics/Math 7-12: Motion
- TExES Physics/Math 7-12: Fluid Mechanics
- TExES Physics/Math 7-12: Linear Momentum
- TExES Physics/Math 7-12: Work, Energy & Power
- TExES Physics/Math 7-12: Laws of Gravitation
- TExES Physics/Math 7-12: Oscillations
- TExES Physics/Math 7-12: Rotational Motion & Conservation of Energy
- TExES Physics/Math 7-12: Heat & Energy
- TExES Physics/Math 7-12: Thermodynamics
- TExES Physics/Math 7-12: Electrical Forces & Fields
- TExES Physics/Math 7-12: Potential & Capacitance
- TExES Physics/Math 7-12: Current Circuits
- TExES Physics/Math 7-12: Magnetism
- TExES Physics/Math 7-12: Waves, Sound & Light
- TExES Physics/Math 7-12: Quantum Physics
- TExES Physics/Mathematics 7-12 Flashcards