Δ YXZ, because A corresponds to Y, B corresponds to X, and C corresponds, to Z.Įxample 3: By what method would each of the triangles in Figures 11 (a) through 11 (i) be proven congruent?įigure 11 Methods of proving pairs of triangles congruent. Theorem 31 (LA Theorem): If one leg and an acute angle of one right triangle are congruent to the corresponding parts of another right triangle, then the triangles are congruent (Figure 9).įigure 9 One leg and an acute angle (LA) of the first right triangle are congruent to theĮxample 2: Based on the markings in Figure 10, complete the congruence statement Δ ABC ≅Δ. Theorem 30 (LL Theorem): If the legs of one right triangle are congruent to the corresponding parts of another right triangle, then the triangles are congruent (Figure 8).įigure 8 The legs (LL) of the first right triangle are congruent to the corresponding parts To the corresponding parts of the second right triangle. Theorem 29 (HA Theorem): If the hypotenuse and an acute angle of one right triangle are congruent to the corresponding parts of another right triangle, then the triangles are congruent (Figure 7).įigure 7 The hypotenuse and an acute angle (HA) of the first right triangle are congruent Postulate 16 (HL Postulate): If the hypotenuse and leg of one right triangle are congruent to the corresponding parts of another right triangle, then the triangles are congruent (Figure 6).įigure 6 The hypotenuse and one leg (HL) of the first right triangle are congruent to theĬorresponding parts of the second right triangle. Theorem 28 (AAS Theorem): If two angles and a side not between them in one triangle are congruent to the corresponding parts in another triangle, then the triangles are congruent (Figure 5).įigure 5 Two angles and the side opposite one of these angles (AAS) in one triangleĪre congruent to the corresponding parts of the other triangle. Postulate 15 (ASA Postulate): If two angles and the side between them in one triangle are congruent to the corresponding parts in another triangle, then the triangles are congruent (Figure 4).įigure 4 Two angles and their common side (ASA) in one triangle are congruent to the Postulate 14 (SAS Postulate): If two sides and the angle between them in one triangle are congruent to the corresponding parts in another triangle, then the triangles are congruent (Figure 3).įigure 3 Two sides and the included angle (SAS) of one triangle are congruent to theĬorresponding parts of the other triangle. 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.
0 kommentar(er)
