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Triangle Congruence Theorems Flashcards

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Questions and Answers

What does the Side Angle Side theorem state?

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

If two angles and a nonincluded side of one triangle are congruent to the corresponding angles and nonincluded side of another triangle, then the triangles are congruent.

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

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. (correct)

What does the Side Side Side theorem state?

If two angles and a nonincluded side of one triangle are congruent to the corresponding angles and nonincluded side of another triangle, then the triangles are congruent.

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

If three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent. (correct)

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.

What does the Angle Side Angle theorem state?

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.

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

If two angles and a nonincluded side of one triangle are congruent to the corresponding angles and nonincluded side of another triangle, then the triangles are congruent.

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. (correct)

What does the Angle Angle Side theorem state?

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

What does the Hypotenuse Leg theorem state?

<p>If the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and a leg of another right triangle, then the triangles are congruent.</p> Signup and view all the answers

Study Notes

Triangle Congruence Theorems

Side Angle Side (SAS) Theorem: 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.
Side Side Side (SSS) Theorem: If three sides of one triangle are congruent to three sides of another triangle, the two triangles are congruent.
Angle Side Angle (ASA) Theorem: 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.
Angle Angle Side (AAS) Theorem: If two angles and a nonincluded side of one triangle are congruent to the corresponding angles and nonincluded side of another triangle, then the triangles are congruent. Example: Angle B is congruent to Angle D, Angle BCA is congruent to Angle DCA, and side AC is congruent to side AC, leading to triangle ABC being congruent to triangle ADC.
Hypotenuse Leg (HL) Theorem: Specifically for right triangles, 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.

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Test your knowledge of triangle congruence theorems with these flashcards. Each card contains a specific theorem and its definition, helping you master the concepts required for geometry. Perfect for students preparing for exams or needing a quick review.