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Proving Triangles Congruent

Proving Triangles Congruent. 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.

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Proving Triangles Congruent

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  1. Proving Triangles Congruent MARK PAUL DE GUZMAN

  2. SSS POSTULATE • SAS POSTULATE • ASA POSTULATE • AAS THEOREM

  3. POSTULATE: Are accepted as true statement and are used to justify conclusions.

  4. THEOREM Statements that must be proven true by citing undefined terms, definitions postulate and previously proven theorems.

  5. SSS POSTULATE: If three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent XY PR YZ XZ PQ RQ and Y P Q X R Z Thus, by SSS Postulate, XYZ PRQ

  6. SIDE ANGLE SIDE POSTULATE • SAS POSTULATE: If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent. GIVEN: BX TP; <B < T; BO TA A P B T X O CONCLUSION: BOX TAP By; SAS POSTULATE

  7. ASA POSTULATE: GIVEN: 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. <P <I ;PA IT;<A <T R F T A P I CONCLUSION: RAP FIT By; ASA POSTULATE

  8. 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.

  9. GIVEN: <A <D ; <B <E ; BC EF B E PROVE: ABC DEF A D C F STATEMENTS: REASONS: • 1. <A <D; <B <E; BC EF • 1. GIVEN • 2. m<A = m<D; m<B = m<E • 2. DEF. OF ANGLES • 3. m<A + m<B + m<C = 180 • m<D + m<E + m<F = 180 3. The Sum of the measures of the interior angles IS 180. • 4. m<A + m<B + m<C = • m<D + m<E + m<F 4. TPE • 5. m<A + m<B+ m<C = • m<A + m<B + m<F 5. Substitution 6. APE • 6. m<C = m<F • 7. DEF. OF ANGLES • 7. <C <F • 8. BC EF 8. GIVEN 9. ∆ABC ∆DEF 9. ASA Postulate

  10. B EXAMPLE 1: GIVEN: ABC is an isosceles ;cut by angle bisector BD PROVE: C A D ABD BDC STATEMENTS: REASONS: 1. BD BD 1. Reflexive Property 2. <C <A 2. Base <‘s of an isosceles are congruent 3. <ADB <DBC 3. Definition of angle bisector 4. ABD BDC 4. AAS THEOREM

  11. EXAMPLE # 2: K GIVEN: KJ II NM ; KJ NM N L <KJL <MNL J PROVE: KJL NML REASONS STATEMENTS M 1. KJ NM 1. GIVEN 2. < KLJ < MLN 2. Vertical Angles are Congruent 3. <KJL <MNL 3.GIVEN 4. KJL NML 4. AAS THEOREM

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