Triangle Congruence Postulates

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Questions and Answers

What does the SSS Postulate state?

If two sides and their included angle in one triangle are congruent to two sides and their included angle in another triangle.
If the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and corresponding leg of another right triangle.
If the sides of one triangle are congruent to the sides of another triangle, then the two triangles are congruent. (correct)
If two angles and their included side in one triangle are congruent to two angles and their included side in another triangle.

What does the SAS Postulate indicate?

If two sides and their included angle in one triangle are congruent to two sides and their included angle in another triangle. (correct)
If the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and corresponding leg of another right triangle.
If the sides of one triangle are congruent to the sides of another triangle.
If two angles and a nonincluded side of one triangle are congruent to the corresponding angles and nonincluded side of another triangle.

What does the ASA Postulate define?

If two sides and their included angle in one triangle are congruent to two sides and their included angle in another triangle.
If the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and corresponding leg of another right triangle.
If the sides of one triangle are congruent to the sides of another triangle.
If two angles and their included side in one triangle are congruent to two angles and their included side in another triangle. (correct)

What does the AAS Postulate assert?

<p>If two angles and a nonincluded side of one triangle are congruent to the corresponding angles and nonincluded side of another triangle. (A)</p> Signup and view all the answers

What does the HL Congruence Theorem state?

<p>If the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and corresponding leg of another right triangle. (D)</p> Signup and view all the answers

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Study Notes

Triangle Congruence Postulates

SSS Postulate: Triangles are congruent if all three corresponding sides are equal in length.
SAS Postulate: Triangles are congruent if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle.
ASA Postulate: Triangles are congruent if two angles and the side between those angles in one triangle are equal to two angles and the corresponding side of another triangle.
AAS Postulate: Triangles are congruent if two angles and a non-included side of one triangle are congruent to the corresponding angles and non-included side of another triangle.
HL Congruence Theorem: For right triangles, if the hypotenuse and one leg of one triangle are equal to the hypotenuse and corresponding leg of another right triangle, the triangles are congruent.