About This Chapter
How it works:
- Identify which concepts are covered on your triangles, theorems and proofs homework.
- Find videos on those topics within this chapter.
- Watch fun videos, pausing and reviewing as needed.
- Complete sample problems and get instant feedback.
- Finish your triangles, theorems and proofs homework with ease!
Topics from your homework you'll be able to complete:
- ASA, SAS and SSS postulates and congruent triangles
- Corresponding parts of congruent triangles are congruent (CPCTC)
- Converse of a statement
- Similarity transformations
- Congruence and similarity in triangles
- Hypotenuse angle (HA) and hypotenuse leg (HL) theorems
- Angle bisector theorem
- Perpendicular bisector theorem
- Congruency of isosceles and right triangles
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. 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.
12. Mathematical Proof: Definition & Examples
Have you ever made a statement that someone challenged you to prove to be true? You have to explain things in a logical and indisputable way in order to do that. In this lesson, you'll learn different ways that statements can be proven in mathematics.
13. Perpendicular Slope: Definition & Examples
Review what perpendicular lines are and what the slope of a line is. Learn about the relationship between slopes of perpendicular lines through definitions and examples.
14. Side-Angle-Side (SAS) Triangle: Definition, Theorem & Formula
In this lesson we will learn about trigonometry and geometry. The SAS theorem ties together those two subjects into a formula which allows us to find the area of a triangle.
15. Square Prism: Definition & Examples
In this lesson, learn what prisms are and what makes square prisms unique. Included are a few examples of square prisms and the qualities that make up these three dimensional objects.
16. Triangle Inequality: Theorem & Proofs
In this lesson, we will use definitions and proofs to learn what the triangle inequality theorem is, why it works, and how to use it to determine if three given line segments can form a triangle.
17. Two-Column Proof in Geometry: Definition & Examples
This lesson will discuss one method of writing proofs, the two-column proof. We will explore some examples and provide some guiding steps you may use to write an effective two-column proof.
18. What is a Vector in Math? - Definition & Examples
This lesson explores vectors, operations with vectors, and modern uses of vectors. Using relevant examples and diagrams, the lesson will demonstrate the applications of vectors in the world.
19. What is an Acute Angle? - Definition, Description & Examples
In this lesson, you'll learn what makes an angle acute and see a few different examples of them. After the lesson, you can test your new knowledge with a brief quiz.
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Other chapters within the High School Geometry: Homework Help Resource course
- Foundations of Geometry: Homework Help
- Logic in Mathematics: Homework Help
- Introduction to Geometric Figures: Homework Help
- Properties of Triangles: Homework Help
- Parallel Lines and Polygons: Homework Help
- Similar Polygons: Homework Help
- Quadrilaterals: Homework Help
- Circular Arcs and Circles: Homework Help
- Conic Sections: Homework Help
- Geometric Solids: Homework Help
- Analytical Geometry: Homework Help
- Introduction to Trigonometry: Homework Help