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MARK PAUL DE GUZMAN SSS POSTULATE SAS POSTULATE ASA POSTULATE AAS THEOREM POSTULATE: Are accepted as true statement and are used to justify conclusions. THEOREM Statements that must be proven true by citing undefined terms, definitions postulate and previously proven theorems. SSS POSTULATE: XY PR YZ Y RQ and XZ PQ P Q X R Z Thus, by SSS Postulate, XYZ PRQ If three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent SIDE ANGLE SIDE SAS POSTULATE: POSTULATE If two sides and the GIVEN: BX TP; <B < T; BO A P B T X O CONCLUSION: BOX By; SAS POSTULATE TA TAP included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent. ASA POSTULATE: GIVEN: <P R <I ;PA IT;<A F T A P CONCLUSION: RAP I FIT By; ASA POSTULATE <T If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then two triangles are congruent. AAS Theorem If two angles and the non-included side of one triangle are congruent, respectively, to the corresponding angles and non-included side of another triangle, then the two triangles are congruent. GIVEN: <A PROVE: <D ; <B ABC <E ; BC DEF STATEMENTS: 1. <A <D; <B EF B A D C REASONS: <E; BC EF E F 1. GIVEN 2. m<A = m<D; m<B = m<E 3. m<A + m<B + m<C = 180 m<D + m<E + m<F = 180 4. m<A + m<B + m<C = m<D + m<E + m<F 5. m<A + m<B+ m<C = m<A + m<B + m<F 6. m<C = m<F 7. <C <F 8. BC EF 2. DEF. OF ANGLES 3. The Sum of the measures of the interior angles IS 180. 4. TPE 9. ∆ABC 9. ASA Postulate ∆DEF 5. Substitution 6. APE 7. DEF. OF 8. GIVEN ANGLES B EXAMPLE 1: GIVEN: ABC is an isosceles angle bisector BD ;cut by PROVE: A ABD BDC STATEMENTS: 1. BD 2. <C 4. REASONS: BD 1. Reflexive Property <A 3. <ADB ABD D 2. Base <‘s of an isosceles are congruent <DBC BDC 3. Definition of angle bisector 4. AAS THEOREM C EXAMPLE # 2: GIVEN: KJ II NM ; KJ <KJL <MNL PROVE: KJL STATEMENTS 1. KJ NM K NM NML L N J REASONS M 1. GIVEN 2. < KLJ < MLN 2. Vertical Angles are Congruent 3. <KJL <MNL 3.GIVEN 4. KJL NML 4. AAS THEOREM