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Sec. 4-2 Δ  by SSS and SAS

Sec. 4-2 Δ  by SSS and SAS. Objective: 1) To prove 2 Δ s  using the SSS and the SAS Postulate. In Sec. 4-1 we learn that if all the sides and all the s are  of 2 Δ s then the Δ s are  . But we don ’ t need to know all 6 corresponding parts are . There are short cuts.

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Sec. 4-2 Δ  by SSS and SAS

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  1. Sec. 4-2Δ by SSS and SAS Objective: 1) To prove 2 Δs  using the SSS and the SAS Postulate

  2. In Sec. 4-1 we learn that if all the sides and all the s are  of 2Δs then the Δs are . • But we don’t need to know all 6 corresponding parts are . • There are short cuts.

  3. 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

  4. 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

  5. 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

  6. 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

  7. 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

  8. 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

  9. 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

  10. Assignment • Page 208 • 1-39 skip any 3

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