Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Question
![**Congruence Postulates Quiz**
**Question:**
Which of the following postulates cannot be used to prove congruence?
**Options:**
A. ASA
B. AAA
C. AAS
D. HL
**Answer Choices:**
- [ ] A
- [ ] B
- [ ] C
- [ ] D
---
**Explanation:**
In this multiple-choice question, students are asked to identify which congruence postulate cannot be used to prove the congruence of triangles. The options provided include:
- **ASA** (Angle-Side-Angle): This postulate states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent.
- **AAA** (Angle-Angle-Angle): This cannot be used to prove congruence as it only shows similarity, not congruence.
- **AAS** (Angle-Angle-Side): This postulate states that if two angles and a non-included side of one triangle are congruent to two angles and a corresponding non-included side of another triangle, then the triangles are congruent.
- **HL** (Hypotenuse-Leg): This postulate applies to right triangles and states that if the hypotenuse and one leg of one right triangle are congruent to the hypotenuse and one leg of another right triangle, then the triangles are congruent.
The correct answer is B. AAA because it does not prove congruence but rather similarity of triangles.
This material is essential for understanding the criteria for proving the congruence of triangles, a fundamental concept in geometry.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F492f8302-2af6-4a90-9bdc-ae62d55032ea%2Fec89252c-aff1-444c-a5d5-3d0f4b2d7d97%2Fxt1hm8n_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Congruence Postulates Quiz**
**Question:**
Which of the following postulates cannot be used to prove congruence?
**Options:**
A. ASA
B. AAA
C. AAS
D. HL
**Answer Choices:**
- [ ] A
- [ ] B
- [ ] C
- [ ] D
---
**Explanation:**
In this multiple-choice question, students are asked to identify which congruence postulate cannot be used to prove the congruence of triangles. The options provided include:
- **ASA** (Angle-Side-Angle): This postulate states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent.
- **AAA** (Angle-Angle-Angle): This cannot be used to prove congruence as it only shows similarity, not congruence.
- **AAS** (Angle-Angle-Side): This postulate states that if two angles and a non-included side of one triangle are congruent to two angles and a corresponding non-included side of another triangle, then the triangles are congruent.
- **HL** (Hypotenuse-Leg): This postulate applies to right triangles and states that if the hypotenuse and one leg of one right triangle are congruent to the hypotenuse and one leg of another right triangle, then the triangles are congruent.
The correct answer is B. AAA because it does not prove congruence but rather similarity of triangles.
This material is essential for understanding the criteria for proving the congruence of triangles, a fundamental concept in geometry.
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