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Proofs: Triangle Congruence (CPCTC, SSS, SAS, ASA, AAS, HL)
The Non-Negotiables
You MUST know...
• The 5 ways to prove congruent triangles (SSS, SAS, ASA, AAS, HL)
• The 2 ways that are NOT appropriate to prove congruence (AAA, SSA/ASS)
• The order of the letters matter when writing congruence statements
• How to setup a geometric proof (most often in a two-column proof)
• The 5 ways to prove congruent triangles (SSS, SAS, ASA, AAS, HL)
• The 2 ways that are NOT appropriate to prove congruence (AAA, SSA/ASS)
• The order of the letters matter when writing congruence statements
• How to setup a geometric proof (most often in a two-column proof)
CPCTC = Corresponding Parts of Congruent Triangles are Congruent
The "parts" are the 3 angles and the 3 line segments that make up a triangle.
Therefore, if we know that
• ∆ABC is congruent to ∆DEF
...then we also know that:
• ∠A and ∠D are congruent
• ∠B and ∠E are congruent
• ∠C and ∠F are congruent
• AB and DE are congruent
• BC and EF are congruent
• AC and DF are congruent
The "parts" are the 3 angles and the 3 line segments that make up a triangle.
Therefore, if we know that
• ∆ABC is congruent to ∆DEF
...then we also know that:
• ∠A and ∠D are congruent
• ∠B and ∠E are congruent
• ∠C and ∠F are congruent
• AB and DE are congruent
• BC and EF are congruent
• AC and DF are congruent
Videos
Interactive Proofs & Geogebra
IXL Sections
On the left side, click the G for Geometry.
Then, work on Sections:
• SSS and SAS (K.1 + K.2)
• ASA and AAS (K.3 + K.4)
• All 4 theorems (K.5 + K.7)
• CPCTC (K.8)
• *** SSS and Distance of a Line (K.6)
Then, work on Sections:
• SSS and SAS (K.1 + K.2)
• ASA and AAS (K.3 + K.4)
• All 4 theorems (K.5 + K.7)
• CPCTC (K.8)
• *** SSS and Distance of a Line (K.6)
Proofs & Proof Blocks
Click HERE to access a PDF that goes through how two-column proofs are set up. They start out with completed examples, then start removing some pieces for you to fill in, and then end with you completing the entire proof.
Click HERE to check out a proof solved using Proof Blocks. This takes the focus off of completing the proof in order, and instead makes sure that you have all of the necessary steps. (The URL is https://vimeo.com/3156012)
Extra Links
http://www.regentsprep.org/regents/math/geometry/gp4/ltriangles.htm
http://www.mathsisfun.com/geometry/triangles-congruent-finding.html
http://www.mathwarehouse.com/geometry/congruent_triangles/
https://www.wyzant.com/resources/lessons/math/geometry/triangles
Practice Writing Proofs
http://www.regentsprep.org/regents/math/geometry/gp4/preprooftriangles.htm
http://www.regentsprep.org/regents/math/geometry/gp4/PracCongTri.htm