About This Chapter
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Students will review:
In this chapter, you'll learn the answers to questions including:
- What are the guiding principles behind the ASA, SAS and SSS postulates?
- How do congruent proofs work?
- What is the converse of a statement?
- How do the AAS, HA and HL proofs work?
- What are the guiding principles behind the angle and perpendicular theorems?
- What procedures are used to prove the 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. Angle of Depression: Definition & Formula
This lesson will explore angles of depression with reference to angles of elevation. Using real world examples, we will seek to understand the similarities and differences of these angles.
13. Law of Syllogism in Geometry: Definition & Examples
This lesson will explain the law of syllogism and provide several examples showing when it can be used to reach a valid conclusion and when it cannot.
14. Midpoint Theorem: Definition & Application
Postulates and proven theorems allow us to know and understand certain things about geometric figures. In this lesson, we will be learning about the Midpoint Theorem.
15. Perpendicular Bisector: Definition, Theorem & Equation
How can we draw a triangle that will have two exactly equal length sides? Or what if we need to find the center of a circle that passes through a given set of points? In this lesson, we'll learn about the perpendicular bisector and how useful it can be in geometry!
16. Proof by Contradiction: Definition & Examples
One of several different ways to prove a statement in mathematics is proof by contradiction. Learn the definition of this method and observe how it is applied to proving a statement's truth value through examples and exploration.
17. Pythagorean Identities in Trigonometry: Definition & Examples
There are three trigonometry identities based on of the Pythagorean theorem. You'll learn what they are in this lesson, as well as how to get from one to the other.
18. Square Matrix: Definition & Concept
A square matrix is a special type of matrix with an equal number of rows and columns. Learn more about square matrices in this lesson, including how to add and multiply them. Then, test your understanding with a short quiz.
19. Tetrahedral in Molecular Geometry: Definition, Structure & Examples
In this lesson, we'll learn what a tetrahedral is in molecular geometry. We'll also look at features and examples of tetrahedral structures. At the end of the lesson, take a brief quiz to see what you learned.
20. Proof by Induction: Steps & Examples
Mathematical induction is a method of proof that is often used in mathematics and logic. We will learn what mathematical induction is and what steps are involved in mathematical induction.
21. Ceva's Theorem: Applications & Examples
Ceva's theorem is an interesting theorem that has to do with triangles and their various parts. This lesson will state the theorem and discuss its application in both real-world and mathematical examples.
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Other chapters within the High School Geometry: Help and Review course
- Foundations of Geometry: Help and Review
- Logic in Mathematics: Help and Review
- Introduction to Geometric Figures: Help and Review
- Properties of Triangles: Help and Review
- Parallel Lines and Polygons: Help and Review
- Similar Polygons: Help and Review
- Quadrilaterals: Help and Review
- Circular Arcs and Circles: Help and Review
- Conic Sections: Help and Review
- Geometric Solids: Help and Review
- Analytical Geometry: Help and Review
- Introduction to Trigonometry: Help and Review