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Bhawna Saini from MODERN SANDEEPNI SCHOOL, asked a question
Subject: Math , asked on 3/10/12

What is  CPCT  in geometry?

Nivedhitha Subramanian From Suguna Rip V School, added an answer, on 7/8/11
42 helpful votes in Math

CPCTC

CPCTC stands for Corresponding Parts of Congruent Triangles are Congruent. It is statement developed from the definition of congruent triangles. It allows us to prove things about the remaining unproven parts of the triangles that we have just proven congruent. It allows us to state correctly after two triangles are congruent, then corresponding parts that were not previously known to be congruent are now allowed to be considered congruent.

Example

Since BO ≅ MA and BW ≅ MN and OW ≅ AN, we can conclude that ΔBOW ≅ ΔMAN because of SSS.

Now we can say ∠B ≅ ∠M, ∠O ≅ ∠A, and ∠W ≅ ∠N because of CPCTC. Since the two triangle were proven congruent, we can now correctly assume that corresponding parts that we knew nothing about, are now congruent.

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Another example

Since BO ≅ MA and OW ≅ AN and ∠O ≅ ∠A, then ΔBOW ≅ ΔMAN by SAS.

Now we can say BW ≅ MN, ∠B ≅ ∠M, and ∠W ≅ ∠N because of CPCTC.

.

Another example

Since BO ≅ MA and ∠B ≅ ∠M and ∠O ≅ ∠A, we can conclude that ΔBOW ≅ ΔMAN because of ASA.

Now we can say ∠W ≅ ∠N, BW ≅ MN and OW ≅ AN because of CPCTC.

.

Another example

Since BO ≅ MA and ∠O ≅ ∠A and ∠W ≅ ∠N, we can conclude that ΔBOW ≅ ΔMAN because of AAS.

Now we can say ∠B ≅ ∠M, BW ≅ MN and OW ≅ AN because of CPCTC.

.

Another example

Since ΔBOW and ΔMAN are right triangle, BO ≅ MA and OW ≅ AN , then ΔBOW ≅ ΔMAN by HL.

Now we can say ∠B ≅ ∠M, ∠O ≅ ∠A, and BW ≅ MN because of CPCTC.

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Remember, we use CPCTC to prove parts are congruent after we have proven triangles congruent. CPCTC is used after SSS, or SAS, or ASA, or AAS, or HL, never before. First we prove that two triangles are congruent. Then if we haven’t already proven that a desired pair of corresponding sides or angles are congruent, we can now do so using CPCTC.

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Pratyush Pant From Khaitan Pub. School, added an answer, on 16/9/09
130 helpful votes in Math


Corresponding Parts of Congruent Triangles.

This means that if 2 triangles are congruent then all the angles and sides of both the triangles will be equal

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Anushka Nafde From Raksha International Public Schhool, added an answer, on 15/9/09
10 helpful votes in Math

 The full form of CPCT is Corresponding Parts of Congruent Triangles.

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EXPERT ANSWER

Ankush Jain , Meritnation Expert added an answer, on 4/10/12

This conversation is already closed by Expert

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Pallavi Barkha From D.a.v.public School, added an answer, on 15/9/09
5 helpful votes in Math

it is th part of 2 congruent triangle which is equal to each other

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Rahul Indra From Sanghmitra Public School, added an answer, on 25/9/11
9 helpful votes in Math

Nivedhithas   kaha se cop y kiya

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Anas From International Indian School, added an answer, on 20/4/12
3 helpful votes in Math

 it is coressponding part of a triangle

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B Kishan From Dav Hzl Sr Sec School, added an answer, on 3/10/12
16 helpful votes in Math

coresponding parts of congurent triangle

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shameem_247... , added an answer, on 22/1/11
1 helpful votes in Math

 corresponding parts of congruent triangles

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sharmaarvin123... , added an answer, on 13/10/10
1 helpful votes in Math

thanks dud to give me this answer .

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Vanshika Bhatia From Basava International School, added an answer, on 3/10/12
1 helpful votes in Math

Corresponding Parts of Congruent Triangles

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Anas From International Indian School, added an answer, on 16/9/11
3 helpful votes in Math

 ty

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nikhilbansal0197... From The Century School, added an answer, on 19/8/11

thanks Nivedhithas

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konicabajaj... From Ajanta Public School, added an answer, on 10/8/12

 yo yo honey singh

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Chaitanya Sagar From Suraj Bhan D A V Public School, added an answer, on 16/9/12

Its cpcte Corresponding Parts of Congruent Triangles are Equal


 

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