![]() ![]() For example: Because you were able to prove that two sides with their included angle were congruent, you would use side-angle-side to prove that the triangles are congruent. Join us as we explore the five triangle congruence theorems (SSS postulate, SAS postulate, ASA postulate, AAS postulate, and HL postulate).Hypotenuse leg (HL): the hypotenuse and one leg of each triangle are equal. ![]() Angle-angle-side (AAS): two angles and a non-included side of each triangle are equal.The two triangles you see on the screen are congruent. The first triangle has an eighty-four degree angle, a side of seven units, and a forty-three degree angle. Play around with the applet to investigate whether non-congruent triangles can be made when we fix certain lengths, or angles. We can say all the biscuits are congruent. Topic: Congruence Use this applet to investigate triangle congruence theorems. Angle-side-angle (ASA): two angles of each triangle and their included side are equal. A simple example is a pack of biscuits with all biscuits of the same size and shape if they are not broken.Side-angle-side (SAS): two sides of the triangle and their included angle (the angle between the two sides) are equal in both triangles. If you can prove that two triangles are congruent, you know that all of their corresponding angles and sides are also congruent.Here, instead of picking two angles, we pick a side and its corresponding side on two triangles. Side-side-side (SSS): both triangles have three sides that equal to each other. By applying the Side Angle Side Postulate (SAS), you can also be sure your two triangles are congruent.Once you have identified all of the information you can from the given information, you can figure out which theorem will allow you to prove the triangles are congruent. Instructions Each triangle congruence theorem uses three elements (sides and angles) to prove congruence. There are five theorems that can be used to prove that triangles are congruent. If the three sides of one triangle are congruent to the corresponding sides of of another triangle, then congruence between the two triangles is established. Choose the correct theorem to prove congruency. ![]()
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