CPCTC, or Corresponding Parts of Congruent Triangles are Congruent, is a principle in geometry that states that when two triangles are congruent, then every corresponding part of one triangle is congruent to the other. This principle is used to justify two triangles being congruent in a proof. The abbreviation CPCTC stands for “Corresponding Parts of Congruent Triangles are Congruent”, and it is used to prove that the diagonals of a rhombus bisect the shape’s angles.
The CPCTC theorem states that if two triangles are congruent, then their corresponding parts, such as the sides and angles that match, are also congruent. For example, if two triangles ABC and DEF are congruent, then their corresponding sides and angles are equal in length and size.
The triangle exterior angle theorem – Corollary states that the measure of an exterior angle of a triangle is greater than the measure of each of its remote interior angles. In summary, CPCTC is a crucial principle in geometry that states that if two or more triangles are congruent, then their corresponding angles and sides are congruent as well.
📹 Exterior Angle Theorem For Triangles, Practice Problems – Geometry
This geometry video tutorial provides a basic introduction into the exterior angle theorem for triangles. It explains how to use it …
📹 CPCTC Geometry Proofs Made Easy, Triangle Congruence – SSS, SAS, ASA, & AAS, Two Colmn Proofs
This video tutorial provides a basic introduction into CPCTC geometry proofs. CPCTC stands for “corresponding parts of …
0:06 SSS≅ Postulate Explanation 0:27 SAS≅ Postulate Explanation 0:40 ASA≅ Postulate Explanation 0:57 AAS≅ Postulate Explanation (1:09 Clarification: HL≅ Postulate is not discussed but is often considered a viable 5th option) 1:13 CPCTC Explanation (1:30 Clarification: second triangle should have the Δ symbol) 2:32 SSS≅ Two Column Proof Example (with CPCTC) 6:15 CPCTC Example (6:19 Clarification: Instead of thinking of CPCTC as the “last step” of a proof, think of CPCTC as the “step after” the triangle congruence step. Proofs can have steps after CPCTC.) 6:53 SAS≅ Two Column Proof Example (with Reflexive Property and CPCTC) (9:38 Clarification: Writing it as segment CB is more appropriate than segment BC because A corresponds to C.) 11:28 SAS≅ Two Column Proof Example (with Radii and Vertical Angles and CPCTC) (12:17 Clarification: Writing it as segment DC is more appropriate than segment CD based on that the rest of the proof is written such that A corresponds to D. Because the triangles are isosceles, the prove statement could still be proved as is, but would require minor adjustments to lines 2, 3, and 4.) (15:10 Mistake: first angle should be AEB, fixed at 17:08) 19:11 ASA≅ Two Column Proof Example (with Parallel Lines and Alternate Interior Angles and Vertical Angles and CPCTC) (20:00 Clarification: Writing it as segment ED is more appropriate than segment DE based on that the rest of the proof is written such that A corresponds to E.) (22:36 Clarification: Writing it as segment EC is more appropriate than segment CE because A corresponds to E.
Here is how I did it. Statement: 1.) Line segment DC is congruent to line segment EA. Reason: 1.) Given. Statement: 2.) Angle 1 is congruent to angle 2. Reason: 2.) Given. Statement: 3.) Line segment AC is congruent to line segment AC. Reason: 3.) Reflexive property Statement: 4.) Triangle ACE is congruent to Triangle CAD. Reason: 4.) Side Angle Side Postulate (Reasons 1 Through 3) Statement: 5.) Line segment AD is congruent to line segment EC. Reason: 5.) Congruent parts of congruent triangles are congruent.
MR. Organic Chemistry Tutor, thank you for another long article/lecture on CPCTC Geometry Proofs Made Easy. I found this Two Column Proof very lengthy and confusing from start to finish. I did not understand this Two column Proof, so I will review this topic for more clarification. There is also an error on line number 8 in the Two Column Proof, a congruent sign is missing.