About This Chapter
WEST Math: Triangle Theorems & Proofs - Chapter Summary
If you'd like to brush up on triangle theorems and proofs as you study for the WEST Math assessment, this chapter offers a number of convenient resources. Entertaining video lessons cover the following concepts:
- The SAS, ASA and SSS postulates
- Proof processes and techniques
- The AAS, HL and HA theorems
- Congruency in right triangles and isosceles triangles
- Perpendicular bisector and angle bisector theorems
Video transcripts highlight key terms and ideas, and lesson quizzes provide a great way to assess your understanding of the material. If you have trouble with any of the concepts presented in this chapter, don't hesitate to reach out to our instructors for clarification.
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 within the NES Mathematics - WEST (304): Practice & Study Guide course
- WEST Math: Properties of Real Numbers
- WEST Math: Fractions
- WEST Math: Decimals & Percents
- WEST Math: Ratios & Proportions
- WEST Math: Units of Measure & Conversions
- WEST Math: Logic
- WEST Math: Reasoning
- WEST Math: Vector Operations
- WEST Math: Matrix Operations & Determinants
- WEST Math: Exponents & Exponential Expressions
- WEST Math: Algebraic Expressions
- WEST Math: Linear Equations
- WEST Math: Inequalities
- WEST Math: Absolute Value
- WEST Math: Quadratic Equations
- WEST Math: Polynomials
- WEST Math: Rational Expressions
- WEST Math: Radical Expressions
- WEST Math: Systems of Equations
- WEST Math: Complex Numbers
- WEST Math: Functions
- WEST Math: Piecewise Functions
- WEST Math: Exponential & Logarithmic Functions
- WEST Math: Continuity of a Function
- WEST Math: Limits
- WEST Math: Rate of Change
- WEST Math: Derivative Rules
- WEST Math: Graphing Derivatives
- WEST Math: Applications of Derivatives
- WEST Math: Area Under the Curve & Integrals
- WEST Math: Integration Techniques
- WEST Math: Applications of Integration
- WEST Math: Foundations of Geometry
- WEST Math: Geometric Figures
- WEST Math: Properties of Triangles
- WEST Math: Parallel Lines & Polygons
- WEST Math: Quadrilaterals
- WEST Math: Circles & Arc of a Circle
- WEST Math: Conic Sections
- WEST Math: Geometric Solids
- WEST Math: Analytical Geometry
- WEST Math: Trigonometric Functions
- WEST Math: Trigonometric Graphs
- WEST Math: Solving Trigonometric Equations
- WEST Math: Trigonometric Identities
- WEST Math: Sequences & Series
- WEST Math: Set Theory
- WEST Math: Statistics Overview
- WEST Math: Summarizing Data
- WEST Math: Tables, Plots & Graphs
- WEST Math: Probability
- WEST Math: Discrete Probability Distributions
- WEST Math: Continuous Probability Distributions
- WEST Math: Sampling
- NES Mathematics WEST Flashcards