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4.6 Using Congruent Triangles

4.6 Using Congruent Triangles. Given: Prove:. given. 1. 1.  BCA   DCA. Def. of angle bisector. 2. 2. given. 3. 3. 4.  BAC   DAC. Def. of angle bisector. 4. 5. Reflexive Prop. 5. 6. 6. ASA. Now that we know the two triangles are congruent, what else can we say?.

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4.6 Using Congruent Triangles

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  1. 4.6 Using Congruent Triangles

  2. Given: Prove: given 1. 1. BCA  DCA Def. of angle bisector 2. 2. given 3. 3. 4. BAC  DAC Def. of angle bisector 4. 5. Reflexive Prop. 5. 6. 6. ASA

  3. Now that we know the two triangles are congruent, what else can we say? B   D Once we have proven triangles are , then we can say all their parts are .

  4. CPCTC corresponding parts of congruent triangles are congruent How can you remember these letters? Cows Poop Cause They Can!

  5. Given: Prove: 1. given 1. 2. Def. of midpt 2. 3. Def. of midpt 3. ECD  BCA 4. 4. Vertical angles 5. 5. SAS cpctc 6. 6.

  6. Given: Prove: 1. given 1. 2. Def. of segment bisector 2. 3. given 3. ADB & CDB are right angles 4. Def. of  lines 4. All right angles are  5. ADB  CDB 5. 6. Reflexive Prop 6. 7. 7. SAS 8. 8. cpctc

  7. Tell which triangles you can show are congruent in order to prove the statement. What postulate or theorem would you use? AAS then CPCTC TSR  LMN

  8. Tell which triangles you can show are congruent in order to prove the statement. What postulate or theorem would you use? SAS then CPCTC JDK  FDE

  9. Tell which triangles you can show are congruent in order to prove the statement. What postulate or theorem would you use? ASA then CPCTC WXZ  YZX

  10. Tell which triangles you can show are congruent in order to prove the statement. What postulate or theorem would you use? then CPCTC HL ABC  DEF

  11. Hints on Proofs If two triangles share a side, then you will probably use the ______________ property. reflexive

  12. Hints on Proofs If you have vertical angles, you will probably use __________ ______ in the proof. vertical angles

  13. Hints on Proofs If you are given “midpoint” or “bisects”, then WILL use __________________, _______________________, or ______________________ in the proof. def. of midpt def. of segment bisector def. of angle bisector

  14. Hints on Proofs If you are given parallel lines, then you will use _______________ _________ angles. alternate interior

  15. Hints on Proofs If you are proving parts of a triangle are congruent, then the proof will end with ____________. cpctc

  16. SSS SAS HL ASA AAS

  17. HW Problem

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