About This Chapter
How It Works:
- Identify the lessons in the Holt McDougal Congruent Triangles chapter with which you need help.
- Find the corresponding video lessons within this companion course chapter.
- Watch fun videos that cover the triangle congruency topics you need to learn or review.
- Complete the quizzes to test your understanding.
- If you need additional help, rewatch the videos until you've mastered the material or submit a question for one of our instructors.
Students will learn:
- Triangle sum properties
- Transformations and congruence
- Congruency proofs
- Different triangle congruence postulates
- Isosceles and equilateral triangle congruency
Holt McDougal is a registered trademark of Houghton Mifflin Harcourt, which is not affiliated with Study.com.
1. Triangles: Definition and Properties
What makes a shape a triangle? In this lesson, we'll explore the definition of a triangle, then analyze the parts of triangles, including the vertices, base and height.
2. Classifying Triangles by Angles and Sides
Not all triangles are the same. There are equilateral, isosceles and scalene triangles. Then there are right, acute and obtuse triangles. In this lesson, we'll learn how to classify triangles using their sides and angles.
3. Interior and Exterior Angles of Triangles: Definition & Examples
Knowing just a few things about the interior or exterior angles of triangles is sometimes all you need to put all the pieces together. Find out more in this lesson.
4. Properties of Congruent and Similar Shapes
In this lesson, we'll look at triangles, rectangles and other shapes that share properties. This includes both congruent and similar shapes. We'll also practice identifying the missing properties of these shapes.
5. Transformations in Math: Definition & Graph
In geometry, transformation refers to the movement of objects in the coordinate plane. This lesson will define and give examples of each of the four common transformations and end with a quiz to make sure you are moving in the right direction.
6. 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.
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. 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. 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.
10. 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.
11. Transformations: How to Shift Graphs on a Plane
What is a transformation? Well, it's something that transforms one function into another! To see what I mean and how that looks, check out this lesson!
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Other chapters within the Holt McDougal Larson Geometry: Online Textbook Help course
- Chapter 1: Essentials of Geometry
- Chapter 2: Reasoning and Proof
- Chapter 3: Parallel and Perpendicular Lines
- Chapter 5: Relationship Within Triangles
- Chapter 6: Similarities
- Chapter 7: Right Triangles and Trigonometry
- Chapter 8: Quadrilaterals
- Chapter 9: Properties of Transformations
- Chapter 10: Properties of Circles
- Chapter 11: Measurements of Figures and Solids
- Chapter 12: Probability