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This section introduces the definition of congruence, outlines several examples of congruent figures, and explains the principles behind the congruence of triangles. It covers the criteria for triangle congruence, such as the SAS, ASA, and SSS rules, emphasizing the significance of corresponding parts in congruent triangles.
In this section, we explore the concept of congruence, primarily focusing on triangles. Congruent figures are those that have identical shapes and sizes. The section highlights that two triangles are congruent if their corresponding sides and angles are equal. Various criteria for triangle congruence are introduced, including:
The concept of congruence is essential in applications such as manufacturing, where identical pieces need to fit together perfectly. Additionally, the section emphasizes the importance of consistent notation when denoting congruent triangles, which includes proper correspondence of their vertices. The section concludes with exercises that reinforce the understanding of triangle congruence through practical examples.
Congruent Figures: Figures that have identical shapes and sizes.
Criteria for Congruence: Rules that help determine whether two triangles are congruent, including SAS, ASA, AAS, SSS, and RHS.
If sides and an angle are the same, then congruence is the name of the game.
Imagine two friends, Amy and Sally, who both have perfectly identical bags. They use them for their identical laptops. Just like their bags, congruent triangles are identical in size and shape.
For triangle congruence remember: SAS, ASA, AAS, SSS. Just think 'Silly Animals Sing Sweetly.'
Two triangles with both pairs of corresponding sides and angles equal are congruent by the criteria of SAS.
If two triangles share a side and have two equal angles adjacent to that side, they are congruent by the ASA criterion.
Term: Congruence
Definition: The property of figures having the same shape and size.
The property of figures having the same shape and size.
Term: SAS Criterion
Definition: A rule stating that two 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.
A rule stating that two 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.
Term: ASA Criterion
Definition: A rule that states that two triangles are congruent if two angles and the side between them are equal in both triangles.
A rule that states that two triangles are congruent if two angles and the side between them are equal in both triangles.
Term: SSS Criterion
Definition: A statement that if three sides of one triangle are equal to three sides of another triangle, the two triangles are congruent.
A statement that if three sides of one triangle are equal to three sides of another triangle, the two triangles are congruent.
Term: AAS Criterion
Definition: A theorem stating that if two angles and a non-included side of one triangle are equal to two angles and the corresponding non-included side of another triangle, the triangles are congruent.
A theorem stating that if two angles and a non-included side of one triangle are equal to two angles and the corresponding non-included side of another triangle, the triangles are congruent.
Term: RHS Criterion
Definition: A rule applying specifically to right triangles; states that if the hypotenuse and one side are equal, the triangles are congruent.
A rule applying specifically to right triangles; states that if the hypotenuse and one side are equal, the triangles are congruent.
Term: CPCT
Definition: Corresponding Parts of Congruent Triangles, meaning that the parts of congruent triangles are equal.
Corresponding Parts of Congruent Triangles, meaning that the parts of congruent triangles are equal.