What is the definition of congruence in geometry?
Congruence Theorems and Properties

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Mathematics
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9th Grade
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Hard
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1.
FLASHCARD QUESTION
Front
Back
Congruence in geometry means that two figures have the same shape and size. This can be shown through congruence statements such as \( \Delta ABC \cong \Delta DEF \).
2.
FLASHCARD QUESTION
Front
What are the three main congruence theorems for triangles?
Back
The three main congruence theorems are: 1) Side-Side-Side (SSS) Congruence Theorem, 2) Side-Angle-Side (SAS) Congruence Theorem, 3) Angle-Side-Angle (ASA) Congruence Theorem.
3.
FLASHCARD QUESTION
Front
What does the Side-Side-Side (SSS) Congruence Theorem state?
Back
The SSS Congruence Theorem states that if three sides of one triangle are equal to three sides of another triangle, then the two triangles are congruent.
4.
FLASHCARD QUESTION
Front
What does the Side-Angle-Side (SAS) Congruence Theorem state?
Back
The SAS Congruence Theorem states that if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, then the two triangles are congruent.
5.
FLASHCARD QUESTION
Front
What does the Angle-Side-Angle (ASA) Congruence Theorem state?
Back
The ASA Congruence Theorem states that if two angles and the included side of one triangle are equal to two angles and the included side of another triangle, then the two triangles are congruent.
6.
FLASHCARD QUESTION
Front
What is the definition of corresponding parts of congruent triangles?
Back
Corresponding parts of congruent triangles are the angles and sides that are in the same relative position in each triangle. If \( \Delta ABC \cong \Delta DEF \), then \( \angle A \cong \angle D \), \( \angle B \cong \angle E \), and so on.
7.
FLASHCARD QUESTION
Front
How can you prove that two triangles are congruent using the Hypotenuse-Leg (HL) Theorem?
Back
The HL Theorem states that if the hypotenuse and one leg of a right triangle are equal to the hypotenuse and one leg of another right triangle, then the two triangles are congruent.
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