About This Chapter
MTEL Math: Triangle Theorems & Proofs - Chapter Summary
In this chapter, you will refresh your understanding of theorems and proofs in geometry so you can feel prepared for these kinds of questions on the MTEL Math exam. After completing this chapter, you will have reviewed:
- Similar triangles
- Triangle congruence theorems
- Congruence proofs
- Statement converses
- Similarity transformations
- Congruence and similarity, and practice problems
- AAS, HA and HL theorems
- Perpendicular bisector and angle bisector theorems
- Congruency of right and isosceles triangles
Each lesson has been designed to review material you are likely to come across on the exam. You'll find a short video included in the lesson to help illustrate the information being explained. The video's transcript is also included for text-based learning. You can take a self-assessment quiz at the end of each lesson to test your knowledge and practice for the exam.
MTEL Math: Triangle Theorems & Proofs Chapter Objectives
The MTEL Math exam is a requirement for educators in Massachusetts who would like to become certified to teach math courses. The exam covers five major areas of content related to math. The information reviewed in this chapter prepares you for questions related to geometry and measurement, which account for 19% of the total score.
The MTEL Math exam is comprised of 100 multiple-choice questions and 2 open-response items. You will have four hours to complete the exam. The open-response question accounts for 20% of the total score and could be related to any of the five content areas. You'll need a score of 240 or higher to qualify for certification.
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 within the MTEL Mathematics (09): Practice & Study Guide course
- MTEL Math: Basic Arithmetic Operations
- MTEL Math: Absolute Value & Integers
- MTEL Math: Fractions
- MTEL Math: Decimals
- MTEL Math: Percents
- MTEL Math: Rates & Ratios
- MTEL Math: Proportions
- MTEL Math: Estimation
- MTEL Math: Origins of Math
- MTEL Math: Rational & Irrational Numbers
- MTEL Math: Complex Numbers
- MTEL Math: Properties of Numbers
- MTEL Math: Exponents & Exponential Expressions
- MTEL Math: Roots & Radical Expressions
- MTEL Math: Scientific Notation
- MTEL Math: Number Theory
- MTEL Math: Number Patterns & Sequences
- MTEL Math: Number Patterns & Series
- MTEL Math: Properties of Functions
- MTEL Math: Graphing Functions
- MTEL Math: Factoring
- MTEL Math: The Coordinate Graph & Symmetry
- MTEL Math: Linear Equations
- MTEL Math: Systems of Linear Equations
- MTEL Math: Vectors, Matrices & Determinants
- MTEL Math: Introduction to Quadratics
- MTEL Math: Working with Quadratic Functions
- MTEL Math: Polynomial Functions Basics
- MTEL Math: Higher-Degree Polynomial Functions
- MTEL Math: Piecewise, Absolute Value & Step Functions
- MTEL Math: Rational Expressions, Functions & Graphs
- MTEL Math: Exponential & Logarithmic Functions
- MTEL Math: Measurement
- MTEL Math: Perimeter & Area
- MTEL Math: Polyhedrons & Geometric Solids
- MTEL Math: Symmetry, Similarity & Congruence
- MTEL Math: Properties of Lines
- MTEL Math: Angles
- MTEL Math: Triangles
- MTEL Math: Similar Polygons
- MTEL Math: The Pythagorean Theorem
- MTEL Math: Quadrilaterals
- MTEL Math: Circles
- MTEL Math: Circular Arcs & Measurement
- MTEL Math: Analytic Geometry & Conic Sections
- MTEL Math: Polar Coordinates & Parameterization
- MTEL Math: Transformations
- MTEL Math: Data & Graphs
- MTEL Math: Statistics
- MTEL Math: Data Collection
- MTEL Math: Samples & Populations
- MTEL Math: Probability
- MTEL Math: Trigonometric Functions
- MTEL Math: Graphs of Trigonometric Functions
- MTEL Math: Trigonometric Identities
- MTEL Math: Applications of Trigonometry
- MTEL Math: Limits
- MTEL Math: Continuity
- MTEL Math: Rate of Change
- MTEL Math: Derivative Calculations & Rules
- MTEL Math: Graphing Derivatives & L'Hopital's Rule
- MTEL Math: Area Under the Curve & Integrals
- MTEL Math: Integration Techniques
- MTEL Math: Integration Applications
- MTEL Math: Differential Equations
- MTEL Math: Discrete & Finite Math
- MTEL Mathematics Flashcards