# Ch 36: TExMaT Master Mathematics Teacher 8-12: Triangle Theorems & Proofs

### About This Chapter

## TExMaT Master Mathematics Teacher 8-12: Triangle Theorems & Proofs - Chapter Summary

Brush up on your geometry knowledge to prepare for TExMaT Master Mathematics Teacher 8-12 exam questions on triangle theorem and proofs. Our expert instructors discuss the use of conditional statements, converse statements and congruence postulates, in addition to proofs, for the following theorems:

- The SAS theorem
- The ASA theorem
- The SSS theorem
- The AAS theorem
- The HA theorem
- The HL theorem
- The perpendicular bisector theorem
- The angle bisector theorem
- The LA and LL theorems

Fun video illustrations and an engaging instructional style make it easy to review all of the triangle theorems and proofs covered on your TExMaT exam. Multiple-choice quizzes are also included with each lesson to help keep your test-prep goals on track.

### TExMaT Master Mathematics Teacher 8-12: Triangle Theorems & Proofs Chapter Objectives

This TExMaT Master Mathematics Teacher 8-12 exam includes a case study essay assignment and 90 multiple-choice questions covering six main content domains. Passing scores qualify applicants for Texas's Master Mathematics Teacher certification for grades 8-12.

Around 18% of exam content addresses geometry and measurement concepts. This chapter can get you ready for questions testing your ability to prove geometric theorems, whether directly or indirectly. After watching these Triangle Theorems & Proofs video lessons, you should also be prepared for questions that measure your understanding of the similarity and congruence concepts used to demonstrate relationships between the sides and angles of two-dimensional shapes.

### 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. 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.

### 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 TExMaT Master Mathematics Teacher 8-12 (089): Practice & Study Guide course

- TExMaT Master Mathematics Teacher 8-12: Properties of Real Numbers
- TExMaT Master Mathematics Teacher 8-12: Fractions
- TExMaT Master Mathematics Teacher 8-12: Decimals & Percents
- TExMaT Master Mathematics Teacher 8-12: Ratios & Proportions
- TExMaT Master Mathematics Teacher 8-12: Measurements & Conversions
- TExMaT Master Mathematics Teacher 8-12: Reasoning & Problem Solving
- TExMaT Master Mathematics Teacher 8-12: Vector Operations
- TExMaT Master Mathematics Teacher 8-12: Matrices & Determinants
- TExMaT Master Mathematics Teacher 8-12: Exponents & Exponential Expressions
- TExMaT Master Mathematics Teacher 8-12: Algebraic Expressions
- TExMaT Master Mathematics Teacher 8-12: Linear Equations
- TExMaT Master Mathematics Teacher 8-12: Inequalities
- TExMaT Master Mathematics Teacher 8-12: Absolute Value Problems
- TExMaT Master Mathematics Teacher 8-12: Quadratic Equations
- TExMaT Master Mathematics Teacher 8-12: Polynomials
- TExMaT Master Mathematics Teacher 8-12: Rational Expressions
- TExMaT Master Mathematics Teacher 8-12: Radical Expressions
- TExMaT Master Mathematics Teacher 8-12: Systems of Equations
- TExMaT Master Mathematics Teacher 8-12: Complex Numbers
- TExMaT Master Mathematics Teacher 8-12: Functions
- TExMaT Master Mathematics Teacher 8-12: Piecewise Functions
- TExMaT Master Mathematics Teacher 8-12: Parametric Equations
- TExMaT Master Mathematics Teacher 8-12: Exponential & Logarithmic Functions
- TExMaT Master Mathematics Teacher 8-12: Continuity of Functions
- TExMaT Master Mathematics Teacher 8-12: Limits
- TExMaT Master Mathematics Teacher 8-12: Rate of Change
- TExMaT Master Mathematics Teacher 8-12: Rules for Calculating Derivatives
- TExMaT Master Mathematics Teacher 8-12: Graphing Derivatives
- TExMaT Master Mathematics Teacher 8-12: Applications of Derivatives
- TExMaT Master Mathematics Teacher 8-12: Area Under the Curve & Integrals
- TExMaT Master Mathematics Teacher 8-12: Integration Techniques
- TExMaT Master Mathematics Teacher 8-12: Integration Applications
- TExMaT Master Mathematics Teacher 8-12: Foundations of Geometry
- TExMaT Master Mathematics Teacher 8-12: Geometric Figures
- TExMaT Master Mathematics Teacher 8-12: Properties of Triangles
- TExMaT Master Mathematics Teacher 8-12: Parallel Lines & Polygons
- TExMaT Master Mathematics Teacher 8-12: Quadrilaterals
- TExMaT Master Mathematics Teacher 8-12: Circular Arcs & Circles
- TExMaT Master Mathematics Teacher 8-12: Conic Sections
- TExMaT Master Mathematics Teacher 8-12: Geometric Solids
- TExMaT Master Mathematics Teacher 8-12: Analytical Geometry
- TExMaT Master Mathematics Teacher 8-12: Trigonometric Functions
- TExMaT Master Mathematics Teacher 8-12: Trigonometric Graphs
- TExMaT Master Mathematics Teacher 8-12: Solving Trigonometric Equations
- TExMaT Master Mathematics Teacher 8-12: Trigonometric Identities
- TExMaT Master Mathematics Teacher 8-12: Sequences & Series
- TExMaT Master Mathematics Teacher 8-12: Data & Statistics
- TExMaT Master Mathematics Teacher 8-12: Summarizing Data
- TExMaT Master Mathematics Teacher 8-12: Tables & Plots
- TExMaT Master Mathematics Teacher 8-12: Probability
- TExMaT Master Mathematics Teacher 8-12: Discrete Probability Distributions
- TExMaT Master Mathematics Teacher 8-12: Continuous Probability Distributions
- TExMaT Master Mathematics Teacher 8-12: Sampling
- TExMaT Master Mathematics Teacher 8-12: Hypothesis Testing
- TExMaT Master Mathematics Teacher 8-12: Regression & Correlation
- TExMaT Master Mathematics Teacher 8-12 Flashcards