TRIANGLE CONGRUENCE | GRADE 8

Learn the different Triangle Congruence Postulates in Geometry. Grade 8 Mathematics. In order to say that two triangles are congruent, you must show that all six pairs of corresponding parts of the two triangles are congruent. However, it is not always necessary to show all the six pairs of congruent parts to prove that the triangles are congruent. These are the postulates and theorem that guarantee the congruence of two triangles by showing only three pairs of congruent corresponding parts. Now, let us see how we can verify if two triangles using two or three pairs of congruent corresponding parts. _____ An included angle lies between two named sides of a triangle. An included side lies between two named angles of the triangle. TRIANGLE CNGRUENCE POSTULATES 1. SSS or Side-Side-Side Congruence Postulate states that: “If three sides of one triangle are congruent to the three corresponding sides of another triangle, then the two triangles are congruent.” Congruence of sides is shown with little hatch marks, like this: ∥. For two triangles,sides may be marked with one, two, and three hatch marks. If △NOM has all three sides equal in measure to the three corresponding sides of △ERS, then the two triangles are congruent by SSS 2. SAS or Side-Angle-Side Congruence Postulate tells us, “If two sides and the included angle of a triangle are congruent to the corresponding two sides and the included angle of another triangle, then the two triangles are congruent.” Two sides and the included angle on △MAR are congruent to the corresponding two sides and included angle on △NIC. So, by SAS, the two triangles are congruent. 3. ASA or Angle-Side-Angle Congruence Postulate says, “If two angles and the included side of a triangle are congruent to the corresponding two angles and the included side of another triangle, then the two triangles are congruent” We have △EDS and △PAU with ∠E ≅ ∠P ̅E̅̅D̅ ≅ ̅P̅̅A̅ ∠D ≅ ∠A by ASA Postulate, these two triangles are congruent.