Geometry Congruent Triangles Geometry Congruent Triangles Congruent triangles are triangles that have the same size and shape. This means that the corresponding sides are equal and the corresponding angles are equal. We can tell whether two triangles are congruent without testing all the sides and all the angles of the two triangles. There are four rules to check for congruent triangles. They are called the SSS rule, SAS rule, ASA rule and AAS rule. There is also another rule for right triangles called the Hypotenuse Leg rule. As long as one of the rules is true, it is sufficient to prove that the two triangles are congruent. SSS Rule :- The Side-Side-Side (SSS) rule states that If three sides of one triangle are equal to three sides of another triangle, then the triangles are congruent. SAS Rule :- The Side-Angle-Side (SAS) rule states that If two sides and the included angle of one triangle are equal to two sides and included angle of another triangle, then the triangles are congruent. ASA Rule :- The Angle-Side-Angle (ASA) Rule states that If two angles and the included side of one triangle are equal to two angles and included side of another triangle, then the triangles are congruent. An included side is the side between the two given angles. Know More About :- Math long Division
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AAS Rule :- The Angle-Angle-Side (AAS) Rule states that If two angles and a non-included side of one triangle are equal to two angles and a non-included side of another triangle, then the triangles are congruent. For the ASA rule the given side must be included and for AAS rule the side given must not be included. The trick is we must use the same rule for both the triangles that we are comparing. Third Angles Theorem In some instances we will need a very significant theorem to help us prove congruence between two triangles. If we know that two angles of two separate triangles are congruent, our inclination is to believe that their third angles are equal because of the Triangle Angle Sum Theorem. This type of reasoning is correct and is a very helpful theorem to use when trying to prove congruence between triangles. The Third Angles Theorem states that if two angles of one triangle are congruent to two angles of another triangle, then the third angles of the triangles are congruent also. Letâ€™s take a look at some exercises to put our knowledge of congruent triangles, CPCTC, and the Third Angles Theorem to work.
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