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It means that if two triangles have two sides with the lengths of the corresponding sides that are equal (congruent) and the angles between between the two sides congruent, then the triangles are congruent (i.e., the three corresponding lengths of sides and three corresponding angles are all congruent).
For example, if you know that triangle one has sides of length 1 and 2 and the angle between the two sides is 60 degrees and that triangle two has sides of length 1 and 2 and the angle between the two sides is 60 degrees, this theorem says that the triangles are congruent, so the length of third side of both triangles is the same and the measure of the other two angles in triangle one is the ame as the measure of the other two angles in triangle two.
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What are the congruence shortcuts?
SSS-side, side, side SAS-side, angle, side ASA-angle, side, angle SAA-side, angle, angle
what- For the given figure, which of the following can be proved using Side-Angle-Side Congruence?
LUE
what- Fill in blank 1 and blank 2 to explain why Angle-Side-Angle Congruence helps imply Angle-Angle-Side Congruence?
(1) third angle, (2) included
Who is the father of congruence of triangles?
The father of congruence of triangles is Euclid, a renowned ancient Greek mathematician known as the "Father of Geometry." In his seminal work, "Elements," Euclid laid down the foundational principles of geometry, including the concept of congruence of triangles. He established the criteria for triangle congruence, such as the Side-Angle-Side (SAS) and Angle-Side-Angle (ASA) postulates, which are still fundamental in modern geometry. Euclid's contributions to the study of triangles and their congruence have had a lasting impact on mathematics and geometric reasoning.
What is SAS Congruence Theorem?
The side-angle-side congruence theorem states that if you know that the lengths of two sides of two triangles are congruent and also that the angle between those sides has the same measure in both triangles, then the two triangles are congruent.
