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In this section, we recap the specific criteria for triangle congruence, including SAS, ASA, AAS, SSS, and RHS rules. Examples are provided to illustrate how these criteria apply, and exercises challenge the understanding of congruence in triangles.
In the study of triangles, congruence is a fundamental concept that signifies two figures having the same shape and size. This section revisits the criteria for establishing the congruence of triangles, which include:
Examples in this section provide practical applications of these criteria, thereby enhancing understanding. Exercises are presented to reinforce these concepts through problem-solving and verification of congruence in various scenarios.
SAS Criterion: Two triangles are congruent if two sides and the included angle are equal.
ASA Criterion: Two triangles are congruent if two angles and the included side are equal.
AAS Criterion: Two triangles are congruent if two angles and a non-included side are equal.
SSS Criterion: Two triangles are congruent if all three sides are equal.
RHS Criterion: In right triangles, if the hypotenuse and one side are equal, then the triangles are congruent.
If two sides and the angle in between align, SAS will proclaim congruence just fine.
Once upon a time in Triangle Town, there were triangles with sides and angles. Whenever two angles and a side connected, they would celebrate their congruent friendship with AAS!
For remembering the criteria: 'SAS for sides and angle in the middle, ASA for angles and side, thatβs a riddle.'
Example applying SAS: If triangle ABC has sides AB = 5 cm, AC = 7 cm and angle A = 60Β°, it is congruent to triangle DEF with the same dimensions.
Example applying AAS: Triangle XYZ has angles of 50Β° and 60Β° with side XY = 10 cm. If triangle PQR has angles of 50Β° and 60Β° and side PQ = 10 cm, then they are congruent.