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Sec. 4-3 Δ  by SSS and SAS

Sec. 4-3 Δ  by SSS and SAS. Mr. Robinson Geometry Fall 2011. Essential Questions:. How do you prove that 2 triangles are congruent: Using the SSS Postulate Using the SAS Postulate.

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Sec. 4-3 Δ  by SSS and SAS

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  1. Sec. 4-3Δ by SSS and SAS Mr. Robinson Geometry Fall 2011

  2. Essential Questions: How do you prove that 2 triangles are congruent: • Using the SSS Postulate • Using the SAS Postulate

  3. In Section 4.2 we learned that if ALL the sides and ALL the angles of two triangles are congruent, then the triangles are congruent. • But we don’t need to know all 6 corresponding parts are . • There are short cuts.

  4. SSS AND SASCONGRUENCE POSTULATES S S S Side MNQR then MNPQRS Side NPRS Side PMSQ POSTULATE 4-1 (SSS) POSTULATE Side -Side -Side (SSS) Congruence Postulate If three sides of one triangle are congruent to three sidesof a second triangle, then the two triangles are congruent. If

  5. P(4-1) SSS (Side-Side-Side) • If 3 sides of one Δ are  to 3 sides of another Δ, then the 2 Δs are . B D F E C A Congruence Statement: ΔABC ΔFDE

  6. Proof: B A • Given: AB  CB AD  CD • Prove: ΔABD ΔCBD C D • Statements • AB  CB • AD  CD • BD  BD • ΔABD ΔCBD • Reasons • Given • Given • Reflection Prop. • SSS S S S

  7. Included – A word used frequently when referring to the s and the sides of a Δ. • Means – “in the middle of” • What  is included between the sides BX and MX? • X • What side is included between B and M? • BM X B M

  8. SSS AND SASCONGRUENCE POSTULATES POSTULATE 4-2 (SAS) Side PQWX A S S then PQSWXY Angle QX Side QSXY POSTULATE Side-Angle-Side (SAS) Congruence Postulate (conjecture 34) If two sides and the included angle of one triangle are congruent to two sides and the included angle of a second triangle, then the two triangles are congruent. If

  9. P(4-2) SAS (Side –Angle – Side) • If 2 sides and the included  of one Δ are  to two sides and the included  of another Δ, then the 2 Δs are . Z S X Y R T Congruence Statement: ΔSTR  ΔZYX

  10. Proof: D B • Given: M is the midpoint of AB A  B & CA  DB • Prove: ΔACM ΔBDM M C • Statements • 1) CA  DB • 2) A  B • M is the midpt of AB • BM  AM • ΔACM ΔBDM • Reasons • Given • Given • Given • Def. of Midpt. • SAS A S A S

  11. Congruent Triangles in the Coordinate Plane H (6, 5) A (-7, 5) C (- 4, 5) G (1, 2) F (6, 2) Use the SSS Postulate to prove that the triangles are congruent. B (-7, 0)

  12. Distance in Calculator

  13. Assignment • Page 216 Problems 6 – 26, 34

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