About This Chapter
How it works:
- Identify the lessons in the McDougal Littell 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 triangles 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:
- The definition and properties of triangles
- Classification of triangles by angles and sides
- Interior and exterior angles of triangles
- Angles of triangle measurement
- Identification of congruent figures and corresponding parts
- Congruence proofs
- Converse of a statement
- Similarity transformations in corresponding figures
- Triangle congruence postulates
- Relationships proofs in figures using congruence and similarity
- The AAS (angle-angle-side) theorem
- Properties of concurrent lines in a triangle
- Use of congruent triangles to prove constructions are valid
- The HA (hypotenuse angle) theorem
- The HL (hypotenuse leg) theorem
- Base angles theorem and converse of the base triangles theorem
- Congruency of isosceles triangles
- Right triangles congruency
- Congruency of equilateral triangles
- Placement of figures in a coordinate plane
- Use of the midpoint formula
- Application of congruent triangles to plan and write proofs
McDougal Littell Geometry 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. 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.
5. 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.
6. 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.
7. 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.
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. Properties of Concurrent Lines in a Triangle
Centroids, orthocenters, incenters, circumcenters, oh my! Don't worry though. In this lesson, we master the various terms for concurrent lines in triangles and match them to altitudes, angle bisectors, perpendicular bisectors and medians.
10. 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.
11. 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.
12. 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.
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. How to Use The Midpoint Formula
The formula for the midpoint of a line segment will tell you how to find the middle of any line segment on the x, y plane. Learn about this formula and see how it is used to find the midpoint of a line segment.
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Other chapters within the McDougal Littell Geometry: Online Textbook Help course
- McDougal Littell Geometry Chapter 1: Basics of Geometry
- McDougal Littell Geometry Chapter 2: Reasoning and Proof
- McDougal Littell Geometry Chapter 3: Perpendicular and Parallel Lines
- McDougal Littell Geometry Chapter 5: Properties of Triangles
- McDougal Littell Geometry Chapter 6: Quadrilaterals
- McDougal Littell Geometry Chapter 7: Transformations
- McDougal Littell Geometry Chapter 8: Similarity
- McDougal Littell Geometry Chapter 9: Right Triangles and Trigonometry
- McDougal Littell Geometry Chapter 10: Circles
- McDougal Littell Geometry Chapter 11: Area of Polygons and Circles
- McDougal Littell Geometry Chapter 12: Surface Area and Volume