We have sent an OTP to your contact. Please enter it below to verify.
Alert
Your message here...
Your notification message here...
For any questions or assistance regarding Customer Support, Sales Inquiries, Technical Support, or General Inquiries, our AI-powered team is here to help!
In this section, we review the important properties of congruent figures, especially triangles, including various rules of congruence like SAS, ASA, AAS, SSS, and RHS. Each concept is essential for understanding the relationships between triangle sides and angles.
In this chapter, we learned that congruence indicates that two figures have both the same shape and size. Key points include the definition of congruence, an overview of congruent pairs such as circles and squares, and a detailed look at triangles. We established several rules of congruence: the SAS (Side-Angle-Side) rule, ASA (Angle-Side-Angle) rule, AAS (Angle-Angle-Side) rule, SSS (Side-Side-Side) rule, and RHS (Right angle-Hypotenuse-Side) rule. Furthermore, we discussed position correspondence of triangle parts and established that angles opposite equal sides in triangles are equal, and sides opposite equal angles are also equal, all while reinforcing these concepts with practical examples.
Congruence: The property where two figures are the same in shape and size.
Angle-Side-Angle (ASA) Rule: A criterion where two angles and the side between them must be equal for triangles to be congruent.
Side-Angle-Side (SAS) Rule: A criterion whereby two sides and the included angle must match for triangles to be considered congruent.
Angle-Angle-Side (AAS) Rule: Pertains to triangles where two angles and a non-included side correspond.
Side-Side-Side (SSS) Rule: The condition that all three sides must be equal for triangle congruence.
Right angle-Hypotenuse-Side (RHS) Rule: Applies specifically to right triangles, where the hypotenuse and one other side must be equal for congruence.
Triangles congruent, angles and sides, match them up, let logic guide!
Once upon a time, two triangle friends were looking for perfect matches, measuring and checking sides and angles, until they found their perfect congruent partners!
Remember SAS - Sides And Shape; satisfies congruence with proper mapping!
Example of ASA: If triangle ABC has angles 50° and 60° and side AB = 5 cm, and triangle DEF has angles 50° and 60° and side DE = 5 cm, then triangles ABC and DEF are congruent by the ASA rule.
Example of SSS: If triangle GHI has sides of 4 cm, 5 cm, and 6 cm, and triangle JKL also has sides of 4 cm, 5 cm, and 6 cm, then GHI is congruent to JKL by the SSS rule.
Term: Congruence
Definition: The quality of being identical in shape and size.
The quality of being identical in shape and size.
Term: SAS Congruence Rule
Definition: A rule that states two triangles are congruent if two sides and the included angle of one triangle are equal to two sides and the included angle of the other triangle.
A rule that states two triangles are congruent if two sides and the included angle of one triangle are equal to two sides and the included angle of the other triangle.
Term: ASA Congruence Rule
Definition: A rule stating that if two angles and the included side of one triangle are equal to two angles and the included side of another triangle, the triangles are congruent.
A rule stating that if two angles and the included side of one triangle are equal to two angles and the included side of another triangle, the triangles are congruent.
Term: AAS Congruence Rule
Definition: A rule that states that if two angles and one side of one triangle are equal to two angles and the corresponding side of another triangle, the triangles are congruent.
A rule that states that if two angles and one side of one triangle are equal to two angles and the corresponding side of another triangle, the triangles are congruent.
Term: SSS Congruence Rule
Definition: A rule stating that if three sides of one triangle are equal to three sides of the other triangle, the triangles are congruent.
A rule stating that if three sides of one triangle are equal to three sides of the other triangle, the triangles are congruent.
Term: RHS Congruence Rule
Definition: A rule applicable to right triangles saying that if the hypotenuse and one side of one triangle are equal to the hypotenuse and one side of another triangle, the triangles are congruent.
A rule applicable to right triangles saying that if the hypotenuse and one side of one triangle are equal to the hypotenuse and one side of another triangle, the triangles are congruent.