Mathematics Quarter 3 - Triangle Congruence

Choose a study mode

Play Quiz
Study Flashcards
Spaced Repetition
Chat to Lesson

Podcast

Play an AI-generated podcast conversation about this lesson

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.

Signup and view all the flashcards

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.

Signup and view all the flashcards

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.

Signup and view all the flashcards

Congruent Triangles

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

Signup and view all the flashcards

Triangle Congruence

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

Signup and view all the flashcards

ASA Congruence Parts

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

Signup and view all the flashcards

ASA Postulate Requirements

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

Signup and view all the flashcards

Included Side

The side that connects two angles of a triangle.

Signup and view all the flashcards

Included Angle

The angle formed by two sides of a triangle.

Signup and view all the flashcards

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.

Signup and view all the flashcards

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.

Signup and view all the flashcards

SSS Congruence Postulate

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

Signup and view all the flashcards

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.

Signup and view all the flashcards

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.

Signup and view all the flashcards

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.

Signup and view all the flashcards

The side opposite angle N

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

Signup and view all the flashcards

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.

Signup and view all the flashcards

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)

Signup and view all the flashcards

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)

Signup and view all the flashcards

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.

Signup and view all the flashcards

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.

Signup and view all the flashcards

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.

Signup and view all the flashcards

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.

Signup and view all the flashcards

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.

Signup and view all the flashcards

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.

Signup and view all the flashcards

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

Use AI to generate personalized quizzes and flashcards to suit your learning preferences.

Quiz Team

Related Documents

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

More Like This

Use Quizgecko on...
Browser
Open
Browser
Browser