About This Chapter
How it works:
- Identify the lessons in the Prentice Hall Geometry 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:
- Identifying congruent figures and corresponding parts
- Converse of a statement
- Similarity transformations in corresponding figures
- Triangle congruence postulates
- Proving relationships in figures
- The AAS (angle-angle-side) theorem
- Congruence proofs
- Congruency of isosceles triangles
- Converse of isosceles triangle theorem
- Congruency of equilateral triangles
- The HL (hypotenuse leg) theorem
- The HA (hypotenuse angle) theorem
- Congruency of right triangles
- Properties of concurrent lines in a triangle
- Using congruent triangles to plan and write proofs
- Using overlapping triangles in proofs
- Using congruent triangles to prove constructions are valid
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1. 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.
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. 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.
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. 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.
6. 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.
7. 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.
8. 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.
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.
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Other chapters within the Prentice Hall Geometry: Online Textbook Help course
- Prentice Hall Geometry Chapter 1: Tools of Geometry
- Prentice Hall Geometry Chapter 2: Reasoning and Proof
- Prentice Hall Geometry Chapter 3: Parallel and Perpendicular Lines
- Prentice Hall Geometry Chapter 5: Relationships Within Triangles
- Prentice Hall Geometry Chapter 6: Quadrilaterals
- Prentice Hall Geometry Chapter 7: Similarity
- Prentice Hall Geometry Chapter 8: Right Triangles and Trigonometry
- Prentice Hall Geometry Chapter 9: Transformations
- Prentice Hall Geometry Chapter 10: Area
- Prentice Hall Geometry Chapter 11: Surface Area and Volume
- Prentice Hall Geometry Chapter 12: Circles