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Transcript
Congruence and Triangles • • • • The two triangle sides to the right are congruent. Theorem 4.3- Third Angles Theorem- This states that if two angles of one triangle are congruent with two angles of another triangle, then the third angles are congruent. Theorem 4.4- Properties of Congruent Triangles- This states that all congruent triangles are either reflexive, symmetric or transitive. Because the two angles are congruent the third angles of the triangles to the right are congruent. Architects many times need to use triangles such as in these buildings. Proving Triangles are Congruent: ASA and AAS AAS Theorem- This states that if two angles and a nonincluded side of one triangle are congruent to two angles and the corresponding nonincluded side of a second triangle, then the two triangles are congruent. ASA Postulate- This states that if two angles and the included side of one triangle are congruent to two angles and the included side of a second triangle, then the two triangles are congruent. Jewelry designers often use triangles in their designs. They may need to prove that they are congruent in order to keep it so that they do not look weird on the wearer. Isosceles, Equilateral, and Right Triangles This chapter shows that if two sides of a triangle are congruent, then the angles opposite them are congruent. The converse of the above statement is also true. These statements are Theorems 4.6 and 4.7 in their respective orders. Artists many times use all forms of triangles in their art. This example has all three forms of angular triangles.