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CHAPTER 4 DOMINOES If the sides of one triangle are congruent to the sides of a second triangle, then the triangles are congruent. P. 206 SSS Postulate AC DF F C AB DE ABC DEF A BC EF B D E If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent. P. 207 SAS Postulate AC DF BC EF F C ABC DEF C F A B D E If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent. P. 207 ASA Postulate A D B E C ABC F DEF AB DE A B D E If two angles and a nonincluded side of one triangle are congruent to the corresponding two angles and side of a second triangle, then the triangles are congruent. P. 214 AAS Theorem (4-5) A D B E AC DF Chapter 4 Theorem Dominoes, page 1 F C ABC DEF A B D E If two sides of a triangle are congruent, then the angles opposite those sides are congruent. P. 222 Isosceles Triangle Theorem (4-6) and (4-7) B AB BC A C C A If two angles of a triangle are congruent, then the sides opposite those angles are congruent. If a triangle is equilateral, then it is equiangular. P. 224 Corollary 4-3 B AB BC AC ABC is equiangular C A If a triangle is equilateral, then each angle measures 60°. P. 224 Corollary 4-3 ABC is equilateral. Chapter 4 Theorem Dominoes, page 2 mA = 60° mB = 60° mC = 60° B 60° A 60° 60° C If a triangle is a right triangle, then one angle is a right angle. P. 180 Definition of Right Triangle B ABC is a right triangle. BCA is a right angle C A If the legs of one right triangle are congruent to the corresponding legs of another right triangle, then the triangles are congruent. P. 245 Theorem 5-5 (LL) DEF and RST are right triangles EF ST D DEF R RST E ED SR F S T If the hypotenuse and an acute angle of one right triangle are congruent to the hypotenuse and corresponding acute angle of another right triangle, then the two triangles are congruent. P. 246 Theorem 5-6 (HA) DEF and RST are right triangles DF RT EDF SRT D DEF R RST E F S T If one leg and an acute angle of one right triangle are congruent to the corresponding leg and acute angle of another right triangle, then the triangles are congruent. P. 247 Theorem 5-7 (LA) DEF and RST are right triangles ED SR DFE RTS D DEF R RST E F S T If the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and corresponding leg of another right triangle, then the triangles are congruent. P. 247 Postulate 5-3 (HL) DEF and RST are right triangles DF RT EF ST Chapter 4 Theorem Dominoes, page 3 D DEF R RST E F S T