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Proving Triangles Congruent

Proving Triangles Congruent. SSS. If we can show all 3 pairs of corr. sides are congruent, the triangles have to be congruent. SAS. Non-included angles. Included angle. Show 2 pairs of sides and the included angles are congruent and the triangles have to be congruent.

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Proving Triangles Congruent

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  1. Proving Triangles Congruent

  2. SSS If we can show all 3 pairs of corr. sides are congruent, the triangles have to be congruent.

  3. SAS Non-included angles Included angle Show 2 pairs of sides and the included angles are congruent and the triangles have to be congruent.

  4. This is called a common side. It is a side for both triangles. We’ll use the reflexive property.

  5. Common side SSS Vertical angles SAS Parallel lines alt int angles Common side SAS

  6. ASA, AAS and HL A ASA – 2 angles and the included side S A AAS – 2 angles and The non-included side A A S

  7. HL ( hypotenuse leg ) is used only with right triangles, BUT, not all right triangles. ASA HL

  8. SOME REASONS WE’LL BE USING • DEF OF MIDPOINT • DEF OF A BISECTOR • VERT ANGLES ARE CONGRUENT • DEF OF PERPENDICULAR BISECTOR • REFLEXIVE PROPERTY (COMMON SIDE) • PARALLEL LINES ….. ALT INT ANGLES

  9. Proof • 1) O is the midpoint of MQ and NP • 2) • 3) • 4) • 1) Given • 2) Def of midpoint • 3) Vertical Angles • 4) SAS Given: O is the midpoint of MQ and NP Prove:

  10. C Given: CX bisects ACB A ˜ B Prove: ∆ACX˜ ∆BCX = 2 1 = AAS B A X P A A S ∆’s CX bisects ACB Given 1 = 2 Def of angle bisc A = B Given CX = CX Reflexive Prop ∆ACX ˜ ∆BCX AAS =

  11. Proof • 1) • 2) • 3) • 1) Given • 2) Reflexive Property • 3) SSS Given: Prove:

  12. Proof • 1) • 2) • 3) • 4) • 1) Given • 2) Alt. Int. <‘s Thm • 3) Reflexive Property • 4) SAS Given: Prove:

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