4.6 Using Congruent Triangles

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

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 .

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

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

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

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

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

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

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

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

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

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

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

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

Ways to Prove Triangles are Congruent SSS SAS HL ASA AAS

HW Problem 4.6 WS 4.6 Worksheet Marking Triangles Worksheet 15-17 Section Page # Assignment Spiral ?s 4.6 WS 4.6 Worksheet Marking Triangles Worksheet 15-17