About This Chapter
SBA Math Grade 8: Triangle Theorems & Proofs
The lessons found in this chapter can help your child as he or she studies triangle theorems and proofs in preparation for the SBA Math 8th Grade exam. The video lessons review all the important concepts and procedures, including:
- Similar triangle applications
- Triangle congruence postulates
- Congruence proofs
- Converse of a statement
- Similarity transformations
- Using congruence and similarity to prove relationships in figures
- The HA, HL and AAS theorems
- Perpendicular bisector and angle bisector theorems
- Congruency of right and isosceles triangles
Video lessons last only about eight minutes on average, and can be viewed from computers, smartphones and tablets. Students can take a short quiz at the end of each lesson to make sure they understand the topics covered.
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.
Earning College Credit
Did you know… We have over 200 college courses that prepare you to earn credit by exam that is accepted by over 1,500 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.
To learn more, visit our Earning Credit Page
Transferring credit to the school of your choice
Not sure what college you want to attend yet? Study.com has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you.
Other chapters within the Smarter Balanced Assessments - Math Grade 8: Test Prep & Practice course
- SBA Math - Grade 8: Basic Arithmetic Operations
- SBA Math - Grade 8: Logic & Mathematical Reasoning
- SBA Math - Grade 8: Number Theory
- SBA Math - Grade 8: Introduction to Fractions
- SBA Math - Grade 8: Operations with Fractions
- SBA Math - Grade 8: Ratios, Rates & Proportions
- SBA Math - Grade 8: Percents
- SBA Math - Grade 8: Introduction to Decimals
- SBA Math - Grade 8: Operations with Decimals
- SBA Math - Grade 8: The Coordinate Graph
- SBA Math - Grade 8: Inequalities
- SBA Math - Grade 8: Factoring
- SBA Math - Grade 8: Rational Numbers
- SBA Math - Grade 8: Roots & Radical Expressions
- SBA Math - Grade 8: Exponents & Exponential Expressions
- SBA Math - Grade 8: Basic Algebraic Expressions
- SBA Math - Grade 8: Writing Algebraic Expressions
- SBA Math - Grade 8: Algebraic Distribution
- SBA Math - Grade 8: Rational Expressions
- SBA Math - Grade 8: Linear Equations
- SBA Math - Grade 8: Systems of Linear Equations
- SBA Math - Grade 8: Properties of Functions
- SBA Math - Grade 8: Graphing Functions
- SBA Math - Grade 8: Symmetry, Similarity & Congruence
- SBA Math - Grade 8: Lines & Angles
- SBA Math - Grade 8: Perimeter & Area
- SBA Math - Grade 8: Surface Area & Volume of Geometric Solids
- SBA Math - Grade 8: Triangles
- SBA Math - Grade 8: Similar Polygons
- SBA Math - Grade 8: The Pythagorean Theorem
- SBA Math - Grade 8: Transformations
- SBA Math - Grade 8: Data & Graphs
- SBA Math - Grade 8: Statistics
- SBA Math - Grade 8: Probability
- SBA Math - Grade 8: Rate of Change
- Smarter Balanced Assessments - Math Grade 8 Flashcards