Postulate 13 (SSS Postulate): If each side of one triangle is congruent to the corresponding side of another triangle, then the triangles are congruent (Figure 2).įigure 2 The corresponding sides (SSS) of the two triangles are all congruent. The following postulates and theorems are the most common methods for proving that triangles are congruent (or equal). To show that two triangles are congruent, it is not necessary to show that all six pairs of corresponding parts are equal. These parts are equal because corresponding parts of congruent triangles are congruent. In Figure, Δ BAT ≅ Δ ICE.Įxample 1: If Δ PQR ≅ Δ STU which parts must have equal measurements? Congruent triangles are named by listing their vertices in corresponding orders. This means that Corresponding Parts of Congruent Triangles are Congruent (CPCTC). The parts of the two triangles that have the same measurements (congruent) are referred to as corresponding parts. The triangles in Figure 1 are congruent triangles. Two triangles are congruent when the three sides and the three angles of one triangle have the same measurements as three sides and three angles of another triangle. Triangles that have exactly the same size and shape are called congruent triangles. Summary of Coordinate Geometry Formulas.Slopes: Parallel and Perpendicular Lines.Similar Triangles: Perimeters and Areas.Proportional Parts of Similar Triangles.Formulas: Perimeter, Circumference, Area.Proving that Figures Are Parallelograms.Triangle Inequalities: Sides and Angles.Special Features of Isosceles Triangles.Classifying Triangles by Sides or Angles.Lines: Intersecting, Perpendicular, Parallel.
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