About This Chapter
How It Works:
- Find the lesson within this chapter that corresponds to what you're studying in the Congruent Triangles chapter of your textbook.
- Watch fun videos that cover the congruent triangle concepts you need to learn or review.
- Complete the quiz after watching each video lesson 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.
You'll learn all of the geometry topics covered in the textbook chapter, including:
- How to classify triangles
- Measuring the angles of triangles
- What an equilateral triangle is
- Geometric theorems
- How to prove triangles are congruent
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1. 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.
2. Measuring the Angles of Triangles: 180 Degrees
Watch this video lesson to see why a triangle's angles always add up to 180 degrees. Also, learn how you can use this unique fact about triangles to find an unknown angle in a triangle.
3. Congruent Polygons: Definition & Examples
In this lesson, you'll review what polygons are, and you'll discover the conditions that polygons must meet in order to be congruent. Then, you can test your knowledge with a brief quiz.
4. 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.
5. Proving the Third Angle Theorem
In this lesson, we examine the Third Angle Theorem in order to prove the values of an unknown angle within a set of similar triangles. After the lesson and a couple of examples, you can test your understanding with a quiz.
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. 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.
8. What is an Equilateral Triangle? - Definition, Properties & Formula
In this lesson, you'll discover what equilateral triangles are and the properties they have that make them unique. You'll also learn two formulas that are associated with equilateral triangles. Then, you can test your knowledge with a brief quiz.
9. 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.
10. Proving Triangles Congruent: Explanation & Examples
If the three sides of one triangle are the same length as the three sides of another triangle and the three angles of the first triangle have the same measure as the angles of the second triangle, then the two triangles are said to be congruent. You can measure all six sides and all six angles to see if they are the same. An easier means of determining if triangles are congruent is to use one of the five triangle congruence theorems.
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Other chapters within the Big Ideas Math Geometry: Online Textbook Help course
- Big Ideas Math Geometry Chapter 1: Basics of Geometry
- Big Ideas Math Geometry Chapter 2: Reasoning and Proofs
- Big Ideas Math Geometry Chapter 3: Parallel and Perpendicular Lines
- Big Ideas Math Geometry Chapter 4: Transformations
- Big Ideas Math Geometry Chapter 6: Relationships Within Triangles
- Big Ideas Math Geometry Chapter 7: Quadrilaterals and Other Polygons
- Big Ideas Math Geometry Chapter 8: Similarity
- Big Ideas Math Geometry Chapter 9: Right Triangles and Trigonometry
- Big Ideas Math Geometry Chapter 10: Circles
- Big Ideas Math Geometry Chapter 11: Circumference, Area, and Volume
- Big Ideas Math Geometry Chapter 12: Probability