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Questions and Answers
What is the minimum number of sides that must be congruent for two triangles to be congruent according to SSS Congruence?
Which congruence criterion involves two sides and the included angle?
What is the minimum number of angles that must be congruent for two triangles to be congruent according to ASA Congruence?
Which of the following is NOT a criterion for triangle congruence?
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What is the specific type of triangle required for HL Congruence?
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If △ABC ≅ △DEF, which of the following must be true?
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Which congruence criterion involves the hypotenuse and one leg of a right triangle?
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What is the main difference between SSS Congruence and SAS Congruence?
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What is the primary condition that must be satisfied to prove the congruence of two triangles using SSS Congruence?
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What is the main advantage of using SSS Congruence over other congruence criteria?
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If two triangles have three sides of equal length, what can be concluded about the triangles?
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What is the key difference between SSS Congruence and other congruence criteria?
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If two triangles are congruent according to SSS Congruence, what can be said about their corresponding angles?
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Study Notes
Triangle Congruence
SSS Congruence
- If three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent.
- This is also known as the Side-Side-Side (SSS) congruence criterion.
- If AB = DE, BC = EF, and AC = DF, then △ABC ≅ △DEF.
SAS Congruence
- 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.
- This is also known as the Side-Angle-Side (SAS) congruence criterion.
- If AB = DE, BC = EF, and ∠A = ∠D, then △ABC ≅ △DEF.
ASA Congruence
- 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.
- This is also known as the Angle-Side-Angle (ASA) congruence criterion.
- If ∠A = ∠D, ∠B = ∠E, and AB = DE, then △ABC ≅ △DEF.
HL Congruence
- If the hypotenuse and one leg of a right triangle are congruent to the hypotenuse and one leg of another right triangle, then the triangles are congruent.
- This is also known as the Hypotenuse-Leg (HL) congruence criterion.
- If △ABC is a right triangle with right angle at C, and △DEF is a right triangle with right angle at F, and AC = DF, and BC = EF, then △ABC ≅ △DEF.
Triangle Congruence
SSS Congruence
- Three sides of one triangle being congruent to three sides of another triangle ensures congruence between the triangles.
- Known as the Side-Side-Side (SSS) congruence criterion.
- Example: If AB = DE, BC = EF, and AC = DF, then △ABC ≅ △DEF.
SAS Congruence
- Two sides and the included angle of one triangle being congruent to two sides and the included angle of another triangle ensures congruence between the triangles.
- Known as the Side-Angle-Side (SAS) congruence criterion.
- Example: If AB = DE, BC = EF, and ∠A = ∠D, then △ABC ≅ △DEF.
ASA Congruence
- Two angles and the included side of one triangle being congruent to two angles and the included side of another triangle ensures congruence between the triangles.
- Known as the Angle-Side-Angle (ASA) congruence criterion.
- Example: If ∠A = ∠D, ∠B = ∠E, and AB = DE, then △ABC ≅ △DEF.
HL Congruence
- The hypotenuse and one leg of a right triangle being congruent to the hypotenuse and one leg of another right triangle ensures congruence between the triangles.
- Known as the Hypotenuse-Leg (HL) congruence criterion.
- Example: If △ABC is a right triangle with right angle at C, and △DEF is a right triangle with right angle at F, and AC = DF, and BC = EF, then △ABC ≅ △DEF.
SSS Congruence
Definition
- SSS Congruence is a criterion for triangle congruence that states if three sides of one triangle are equal to three sides of another triangle, the triangles are congruent.
Key Points
- Also known as the "Side-Side-Side" congruence criterion.
- It is a sufficient condition for triangle congruence.
How it Works
- Identify the three sides of one triangle and the corresponding three sides of another triangle.
- Check if the three sides of one triangle are equal to the three sides of the other triangle.
- If all three sides are equal, the triangles are congruent.
Example
- If AB = DE, BC = EF, and AC = DF, then ∆ABC ≅ ∆DEF, meaning triangles ABC and DEF are congruent.
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Description
Learn about SSS and SAS congruence criteria for triangle congruence, including the conditions and rules for congruent triangles.
