About This Chapter
How it works:
- Identify the lessons in Glencoe Geometry's Congruent Triangles chapter with which you need help.
- Find the corresponding video lessons within this companion course chapter.
- Watch fun videos that cover the congruent triangle topics you need to learn or review.
- Complete the quizzes to test your understanding.
- If you need additional help, re-watch the videos until you've mastered the material or submit a question for one of our instructors.
Students will learn:
- Categories and properties of triangles
- Exterior and interior angles of triangles
- The third angle theorem
- Characteristics of congruent and similar shapes
- Congruent proofs for triangles
- Triangle congruence postulates
- The angle-angle-side theorem
- The hypotenuse angle theorem
- The hypotenuse leg theorem
- Geometric constructions
- Congruency of isosceles and right triangles
- Characteristics of equilateral triangles
Glencoe Geometry is a registered trademark of McGraw-Hill, 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. 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.
5. Angles and Triangles: Practice Problems
Want more practice solving with angle pairs? How about more review for solving angles in triangles? Look no further. Get more practice here, and test your ability with a quiz.
6. 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.
7. 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.
8. 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.
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. Constructing Triangles: Types of Geometric Construction
When you're asked to construct a triangle, it's time to break out that compass and straight edge! In this lesson, find out how to construct triangles no matter what you're given.
11. 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.
12. 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.
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.
15. 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.
16. Triangles in Coordinate Planes & Proofs
When you draw a triangle in a coordinate plane, you can use the coordinates on the plane to find information about the triangle. You can even do proofs with triangles in a plane. Watch this lesson to learn how.
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Other chapters within the Glencoe Geometry: Online Textbook Help course
- Glencoe Geometry Chapter 1: Points, Lines, Planes, and Angles
- Glencoe Geometry Chapter 2: Reasoning and Proof
- Glencoe Geometry Chapter 3: Parallel and Perpendicular Lines
- Glencoe Geometry Chapter 5: Relationships in Triangles
- Glencoe Geometry Chapter 6: Proportions and Similarity
- Glencoe Geometry Chapter 7: Right Triangles and Trigonometry
- Glencoe Geometry Chapter 8: Quadrilaterals
- Glencoe Geometry Chapter 9: Transformations
- Glencoe Geometry Chapter 10: Circles
- Glencoe Geometry Chapter 11: Area and Volume
- Glencoe Geometry Chapter 12: Surface Area
- Glencoe Geometry Chapter 13: Volume