Mathematics Quarter 3 - Triangle Congruence
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Questions and Answers

Which statement is true regarding triangle congruence?

  • Congruence can be proven using only angle measurements.
  • Two triangles cannot be congruent if they have different side lengths.
  • Two triangles are congruent if all corresponding parts are congruent. (correct)
  • Two triangles can be congruent even if only one angle is congruent.

    • Angle-Angle-Angle (AAA) can be used as a test for triangle congruence.

    False (B)

    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.

    <p>Hypotenuse-Leg</p> Signup and view all the answers

    Match the following congruence postulates with their definitions:

    <p>ASA = Two angles and the included side are congruent. SAS = Two sides and the included angle are congruent. SSS = All three sides of one triangle are congruent to the three sides of another triangle. HyL = A hypotenuse and a leg of a right triangle are congruent.</p> Signup and view all the answers

    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?

    <p>SAS Congruence Postulate (B)</p> Signup and view all the answers

    Two triangles are congruent if only their angles are congruent.

    <p>False (B)</p> Signup and view all the answers

    What does the SSS Congruence Postulate state?

    <p>If three sides of one triangle are congruent to the three sides of another triangle, then the two triangles are congruent.</p> Signup and view all the answers

    The theorem that proves congruence by using the legs of two right triangles is called the _____ Congruence Theorem.

    <p>LL</p> Signup and view all the answers

    Which of the following describes the ASA Congruence Postulate?

    <p>Two angles and the included side are congruent. (C)</p> Signup and view all the answers

    The Leg-Angle (LA) Congruence Theorem applies only to right triangles.

    <p>True (A)</p> Signup and view all the answers

    State the theorem that guarantees congruency if two angles and the included side of one triangle are congruent to another triangle.

    <p>ASA Congruence Postulate</p> Signup and view all the answers

    According to the congruence postulates, two triangles are congruent if their corresponding _____ and _____ are congruent.

    <p>sides, angles</p> Signup and view all the answers

    Which of the following statements is true regarding triangle congruence?

    <p>Two triangles are congruent if their corresponding sides and angles are congruent. (A)</p> Signup and view all the answers

    What is the included side of angles ∠R and ∠P in triangle PRQ?

    <p>RP (C)</p> Signup and view all the answers

    The included angle of sides AB and AC in triangle ABC is ∠B.

    <p>False (B)</p> Signup and view all the answers

    Name the opposite angle of side BC in triangle ABC.

    <p>∠A</p> Signup and view all the answers

    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.

    <p>included</p> Signup and view all the answers

    Match the following congruence postulates to their descriptions:

    <p>SAS = Two sides and the included angle are congruent ASA = Two angles and the included side are congruent AAS = Two angles and a non-included side are congruent SSS = All three sides are congruent</p> Signup and view all the answers

    Which of the following is NOT a postulate for proving triangle congruence?

    <p>AA (D)</p> Signup and view all the answers

    To prove that two triangles are congruent, it is necessary to show that all six pairs of corresponding parts are congruent.

    <p>False (B)</p> Signup and view all the answers

    In triangle ABC, what is the included angle of sides AB and AC?

    <p>∠A</p> Signup and view all the answers

    The opposite side of angle ∠A in triangle ABC is ______.

    <p>BC</p> Signup and view all the answers

    In triangle MPQ, if MP ≅ RS, ∠P ≅ ∠S, and PN ≅ SQ, what can be concluded?

    <p>The triangles are congruent by SAS. (A)</p> Signup and view all the answers

    Two triangles are congruent if and only if all of their corresponding parts are similar.

    <p>False statement (C)</p> Signup and view all the answers

    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.

    <p>included side</p> Signup and view all the answers

    Which method is used to prove the congruency of triangles if BD is the common side?

    <p>SAS (D)</p> Signup and view all the answers

    If ∆MAN ≅ ∆BOY, what is the measure of angle A?

    <p>Angle B</p> Signup and view all the answers

    Flashcards

    Opposite side of an angle

    The side of a triangle that is opposite an angle.

    Opposite angle of a side

    The angle of a triangle that is opposite a side.

    Included side of two angles

    The side of a triangle that lies between two angles.

    Included angle of two sides

    The angle of a triangle that lies between two sides.

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    SAS (Side-Angle-Side) Congruence Postulate

    A postulate that states: 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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    ASA (Angle-Side-Angle) Congruence Postulate

    A postulate that states: If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.

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    Congruent Triangles

    The relationship where all corresponding sides and angles of two triangles are congruent.

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    Triangle Congruence

    Proving that two triangles are congruent by showing that three specific pairs of corresponding parts are congruent.

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    ASA Congruence Parts

    The three pairs of corresponding parts needed to prove triangle congruence using ASA Postulate.

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    ASA Postulate Requirements

    Two angles and the included side of one triangle are congruent to the corresponding parts of the other triangle.

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    Included Side

    The side that connects two angles of a triangle.

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    Included Angle

    The angle formed by two sides of a triangle.

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    SAS Congruence 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 two triangles are congruent.

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    ASA Congruence 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 two triangles are congruent.

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    SSS Congruence Postulate

    If three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent.

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    Hypotenuse-Angle (HyA) Congruence Theorem

    Two triangles are congruent if the hypotenuse and one acute angle of one triangle are congruent to the hypotenuse and corresponding acute angle of the other.

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    Hypotenuse-Leg (HyL) Congruence Theorem

    Two triangles are congruent if the hypotenuse and one leg of one triangle are congruent to the hypotenuse and corresponding leg of the other.

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    Angle-Angle-Angle (AAA) Congruence

    Knowing the three angles of a triangle are equal to those in another triangle does not guarantee the triangles are congruent.

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    The side opposite angle N

    The side opposite to angle N in a triangle. It's the side that does not touch angle N.

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    The angle opposite PM

    The angle opposite side PM in a triangle. It's the angle that does not share any side points with PM.

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    Leg-Leg (LL) Congruence Theorem

    If the legs of one right triangle are congruent to the legs of another right triangle, then the triangles are congruent. (LL)

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    Leg-Angle (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 triangles are congruent. (LA)

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    Congruence Statement

    Indicates the order in which angles and sides correspond in congruent triangles. For example, if triangle ABC is congruent to triangle DEF, it means angle A corresponds to angle D, angle B corresponds to angle E, etc.

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    Theorem

    A theorem is a proved statement that can be used to derive other statements. It's a foundational rule in mathematics which is backed by rigorous proof.

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    HyL Congruence Theorem

    If the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and a leg of another right triangle, then the two triangles are congruent.

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    HyA Congruence Theorem

    If the hypotenuse and an acute angle of one right triangle are congruent to the hypotenuse and an acute angle of another right triangle, then the two triangles are congruent.

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    LL Congruence Theorem

    If two legs of one right triangle are congruent to two legs of another right triangle, then the two triangles are congruent.

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    LA Congruence Theorem

    If one leg and an acute angle of one right triangle are congruent to one leg and an acute angle of another right triangle, then the two triangles are congruent.

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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

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    Related Documents

    Mathematics Quarter 3 – Module 2 (Week 3 & 4) PDF

    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.

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