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Questions and Answers
Which statement is true regarding triangle congruence?
Which statement is true regarding triangle congruence?
Angle-Angle-Angle (AAA) can be used as a test for triangle congruence.
Angle-Angle-Angle (AAA) can be used as a test for triangle congruence.
False
What does the included angle of a triangle refer to?
What does the included angle of a triangle refer to?
The angle formed between two sides of the triangle.
The __________ theorem states that if the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and corresponding leg of another right triangle, then the triangles are congruent.
The __________ theorem states that if the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and corresponding leg of another right triangle, then the triangles are congruent.
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Match the following congruence postulates with their definitions:
Match the following congruence postulates with their definitions:
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Which postulate states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent?
Which postulate states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent?
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Two triangles are congruent if only their angles are congruent.
Two triangles are congruent if only their angles are congruent.
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What does the SSS Congruence Postulate state?
What does the SSS Congruence Postulate state?
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The theorem that proves congruence by using the legs of two right triangles is called the _____ Congruence Theorem.
The theorem that proves congruence by using the legs of two right triangles is called the _____ Congruence Theorem.
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Which of the following describes the ASA Congruence Postulate?
Which of the following describes the ASA Congruence Postulate?
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The Leg-Angle (LA) Congruence Theorem applies only to right triangles.
The Leg-Angle (LA) Congruence Theorem applies only to right triangles.
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State the theorem that guarantees congruency if two angles and the included side of one triangle are congruent to another triangle.
State the theorem that guarantees congruency if two angles and the included side of one triangle are congruent to another triangle.
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According to the congruence postulates, two triangles are congruent if their corresponding _____ and _____ are congruent.
According to the congruence postulates, two triangles are congruent if their corresponding _____ and _____ are congruent.
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Which of the following statements is true regarding triangle congruence?
Which of the following statements is true regarding triangle congruence?
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What is the included side of angles ∠R and ∠P in triangle PRQ?
What is the included side of angles ∠R and ∠P in triangle PRQ?
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The included angle of sides AB and AC in triangle ABC is ∠B.
The included angle of sides AB and AC in triangle ABC is ∠B.
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Name the opposite angle of side BC in triangle ABC.
Name the opposite angle of side BC in triangle ABC.
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The SAS congruence postulate states that if two sides and the ______ angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent.
The SAS congruence postulate states that if two sides and the ______ angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent.
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Match the following congruence postulates to their descriptions:
Match the following congruence postulates to their descriptions:
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Which of the following is NOT a postulate for proving triangle congruence?
Which of the following is NOT a postulate for proving triangle congruence?
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To prove that two triangles are congruent, it is necessary to show that all six pairs of corresponding parts are congruent.
To prove that two triangles are congruent, it is necessary to show that all six pairs of corresponding parts are congruent.
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In triangle ABC, what is the included angle of sides AB and AC?
In triangle ABC, what is the included angle of sides AB and AC?
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The opposite side of angle ∠A in triangle ABC is ______.
The opposite side of angle ∠A in triangle ABC is ______.
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In triangle MPQ, if MP ≅ RS, ∠P ≅ ∠S, and PN ≅ SQ, what can be concluded?
In triangle MPQ, if MP ≅ RS, ∠P ≅ ∠S, and PN ≅ SQ, what can be concluded?
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Two triangles are congruent if and only if all of their corresponding parts are similar.
Two triangles are congruent if and only if all of their corresponding parts are similar.
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In a triangle, when the vertices of the two angles are the endpoints of the segment, the segment is said to be the ______________ of the two angles.
In a triangle, when the vertices of the two angles are the endpoints of the segment, the segment is said to be the ______________ of the two angles.
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Which method is used to prove the congruency of triangles if BD is the common side?
Which method is used to prove the congruency of triangles if BD is the common side?
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If ∆MAN ≅ ∆BOY, what is the measure of angle A?
If ∆MAN ≅ ∆BOY, what is the measure of angle A?
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Study Notes
Mathematics Quarter 3 - Module 2 (Week 3 & 4) - Triangle Congruence
- This module covers triangle congruence
- The module is designed to help students master triangle congruence concepts
- The language used in the module is designed for diverse learning levels
- The lessons are organized in the standard order of the course
- The order of the lessons can be adjusted to fit the textbook being used
- The module contains a pre-test, several examples, postulates and theorems relating to Triangle Congruence
Lesson 1: Triangle Congruence
- After completing this module, students are expected to:
- Illustrate triangle congruence
- Illustrate SAS, ASA, and SSS congruence postulates
- This module introduces the fundamental concepts of triangle congruence in real-world applications
What I Know (Pre-Test)
- Question 1: Two triangles are congruent if all corresponding parts are similar (False)
- Question 2: In a triangle, a segment between the endpoints of two angles is the included side
- Question 3: The SSS congruence postulate means if three sides of one triangle are congruent to three sides of another, the triangles are congruent
- Question 4: The provided figures are not related to the Hypotenuse-Angle theorem
- Question 5: If ADBA ↔ AFEG, then ∠EGF corresponds to ∠CBD
- Question 6: If triangles are congruent, then congruent sides and angles are equal but not all statements are always true (for instance AFEG = ABCD is not necessarily true)
Congruence Postulates and Theorems
- SSS Postulate: If three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent.
- SAS Postulate: If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent
- ASA Postulate: 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
- LA Congruence Theorem: If a leg and an acute angle of one right triangle are congruent to a leg and an acute angle of another right triangle, then the two triangles are congruent.
- LL Congruence Theorem: If the legs of one right triangle are congruent to the legs of another right triangle, then the two triangles are congruent.
- HyA Congruence Theorem: If the hypotenuse and an acute angle of one right triangle are congruent to the hypotenuse and a corresponding acute angle of another right triangle, then the two triangles are congruent.
- HyL Congruence Theorem: If the hypotenuse and a leg of one right triangle are congruent to the corresponding hypotenuse and leg of another right triangle, then the triangles are congruent
- AAA (Angle-Angle-Angle) is not a test for triangle congruence
Illustrative Examples
- Illustrative examples are provided to show how to identify corresponding parts of congruent triangles and apply the various postulates and theorems
Assessment (Post-Test)
- Questions on congruent triangles, corresponding sides and angles
- Application of congruence postulates and theorems
Studying That Suits You
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Related Documents
Description
This module covers the concept of triangle congruence in mathematics. Designed for students, it includes pre-tests, examples, postulates, and theorems related to triangle congruence. By the end, learners should master the SAS, ASA, and SSS congruence criteria with real-world applications.
