Transcript cpctc
I Have CPCTC by Karadimos, MD I woke up this morning not feeling like I should. The doctor told me it's not good. Something has happened to me. I came down with CPCTC. Doc said, "When your triangles became identical, your corresponding parts measured equal." Triangle Congruence I said, "When corresponding parts were the same, congruent triangles were to blame." The bad news is, CPCTC is very contagious. The good news is, you can use it to be courageous. Solving proofs can be tough. SSS, SAS, ASA, AAS isn't always enough. CPCTC is the next device. You'll hear Karadimos, MD give that advice. The test for CPCTC, is to examine the geometry. Congruent triangles is the start. CPCTC is the very next part. To find the cure for the CPCTC blues, wait for non-congruent triangles to hit the news. Doctors have no pills, for my CPCTC ills. Triangle Congruence Theorem In geometry, CPCTC is the abbreviation of a theorem involving congruent triangles. CPCTC stands for Corresponding Parts of Congruent Triangles are Congruent. CPCTC states that if two or more triangles are congruent, then all of their corresponding parts are congruent as well. If ABC DEF then, AB DE , BC EF , AC DF A D, B E , C F Notes: Example proofs Given : AB DE ;B E , BC EF Prove : CA FD Statements Reasons 1. AB DE (S) 1. Given 2.B E (A) 2. Given 3.BC EF (S) 3. Given 4.ABC DEF 4. SAS SAS 5.CA FD 5. CPCTC Another Example proof Given:E is the midpoint of BD BD bisects AC Prove : B D Statements Reasons 1. E is the midpoint of BD 1. Given BD bisects AC 2. BE DE (S) 3.BEA DEC 4. AE CE 5.BEA DEC 6.B D (A) (S) 2. A midpoint divides a segment into 2 congruent segments. 3. Vertical angles are congruent. 4.A segment bisector divides a segment into 2 congruent segments. 5.SAS SAS 6. CPCTC Given : AF is the perpendicu lar bisector of GI ; 1 2; FO FT Prove : O T Statements G Reasons 1. AF is the perpendicu lar bisector of GI 1. GIVEN 2. 1 2 2. GIVEN 1 F I 3.FO FT (S) 4.GF IF (S) 5. GFA and IFA are right angles. 3. GIVEN 4. Definition of segment bisector 5. Definition of perpendicular lines 6. GFA IFA 6. All right angles are congruent. 7. mGFA m1 mGFO mIFA m2 mIFT 7. Partition postulate 8. m1 mGFO m2 mIFT 8. Substitution Property 9. GFO IFT (A) 9. Subtraction Property of equality 10. GFO IFT 10. SAS SAS 11. O T 11. CPCTC O A 2 T Why was the obtuse angle upset? Because he was never right!!!! What do you get when you cross geometry with McDonalds? A plane cheeseburger!