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G.CO.B.8 STUDENT NOTES & PRACTICE WS #4 – geometrycommoncore.com 1 In objective G.CO.B.7 we discussed how if two triangles are congruent to each other there are a number of other things that we know – that the corresponding angles and sides are also congruent. In the proofs below we you might notice that the ‘PROVE’ item is not to prove two triangles congruent…. It is to prove two corresponding pieces (angles or sides) to be congruent. The general strategy will be to first prove triangles to be congruent so that we can make a statement about sides or angles also being congruent. We often use the abbreviation CPCTC as a reason for stating corresponding sides or angle to be congruent – it stands for: CPCTC – Corresponding Parts of Congruent Triangles are Congruent. ABC DEF A congruence statement for triangles relates one identical object to another by identifying the corresponding parts that match each other. AB DE A D BC EF B E CA FD C F Prove the following relationships. GIVEN: AB || DE & BC DC PROVE: AC EC GIVEN: AC EC & B A E C D STATEMENT 1. AB || DE 2. BC DC 3. B D 4. A E 5. ABC EDC 6. AC EC REASON 1. Given 2. Given 3. || Alt. Int. 4. || Alt. Int. 5. AAS 6. CPCTC BC DC PROVE: B D STATEMENT 1. AC EC 2. BC DC 3. BCA DCE 4. BCA DCE 5. B D E B C A D REASON 1. Given 2. Given 3. Vertical 4. SAS 5. CPCTC G.CO.B.8 STUDENT NOTES & PRACTICE WS #4 – geometrycommoncore.com NYTS (Now You Try Some) Prove the following relationships. 1. GIVEN: B AC bisects DAB A & AB AD C PROVE: D B D STATEMENT REASON 1. Given 1. AC bisects DAB 2. AB AD 2. Given 3. BAC DAC 3. Def. Bisector 4. AC AC 5. ABC ADC 6. B D 4. Reflexive Prop. 5. SAS 6. CPCTC 2. GIVEN: C is the midpoint of AE & BD PROVE: AB DE STATEMENT 1. C is the midpoint of AE & BD 2. AC EC 3. BC DC 4. BCA DCE 5. ABC EDC 6. AB DE 2 B A E C D REASON 1. Given 2. Def. of Midpoint 3. Def. of Midpoint 4. Vertical 5. SAS 6. CPCTC