Triangle Congruence Rules Flashcards

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Questions and Answers

What does the Side-Side-Side (SSS) Congruence Theorem state?

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.
If three sides of one triangle are congruent to three sides of another triangle, then these two triangles are congruent. (correct)
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.
If two sides and the included angle of one triangle are congruent to the corresponding parts of another triangle, then the triangles are congruent.

What does the Side-Angle-Side (SAS) Congruence Theorem state?

If two sides and the included angle of one triangle are congruent to the corresponding parts of another triangle, then the triangles are congruent. (correct)
If two angles and the non-included side of one triangle are congruent to two angles and the non-included side of another triangle, then these two triangles are congruent.
If three sides of one triangle are congruent to three sides of another triangle, then these two triangles are congruent.
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.

What does the Angle-Side-Angle (ASA) Congruence Theorem state?

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.

What does the Angle-Angle-Side (AAS) Congruence Theorem state?

<p>If two angles and the non-included side of one triangle are congruent to two angles and the non-included side of another triangle, then these two triangles are congruent.</p> Signup and view all the answers

What does the HL theorem state?

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

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Study Notes

Triangle Congruence Criteria

Side-Side-Side (SSS):
- States that congruence of all three sides of two triangles ensures their overall congruence.
Side-Angle-Side (SAS):
- Establishes that if two sides and the included angle of one triangle match those of another triangle, the triangles are congruent.
Angle-Side-Angle (ASA):
- Claims that congruence of two angles and the side between them leads to congruence of the triangles; the side must be the one formed by the two angles.
Angle-Angle-Side (AAS):
- Involves two angles and a non-included side; if these components are congruent in two triangles, the triangles are congruent.
Hypotenuse-Leg (HL):
- Applies specifically to right triangles, stating that if the hypotenuse and one leg of one triangle are congruent to the corresponding parts of another right triangle, then the triangles are congruent.