The CPCTC theorem states that as soon as two triangles space congruent, their matching parts are equal. The CPCTC is an abbreviation offered for 'corresponding components of congruent triangles space congruent'.

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 1 What is CPCTC? 2 CPCTC Triangle Congruence 3 CPCTC Proof 4 FAQs on CPCTC

The abbreviation CPCTC is because that Corresponding parts of Congruent Triangles space Congruent. The CPCTC theorem states that when two triangles space congruent, then every corresponding part of one triangle is congruent come the other. This means, when two or much more triangles room congruent climate their equivalent sides and angles are also congruent or equal in measurements. Let us know the definition of congruent triangles and also corresponding components in detail.

Congruent Triangles

Two triangles are claimed to it is in congruent if castle have exactly the exact same size and the same shape. 2 congruent triangles have actually three equal sides and also equal angles v respect to each other.

Corresponding Parts

Corresponding sides average the three sides in one triangle room in the same position or spot together in the other triangle. Equivalent angles average the 3 angles in one triangle are in the same position or spot as in the other triangle.

In the provided figure, △ABC ≅ △LMN. It way that the 3 pairs that sides and three bag of angles of △ABC are equal to the three pairs of corresponding sides and also three bag of matching angles that △LMN.

In these two triangles ABC and also LMN, let us identify the 6 parts: i.e. The three corresponding sides and also the three equivalent angles. Abdominal corresponds come LM, BC synchronizes to MN, AC coincides to LN. ∠A synchronizes to ∠L, ∠B synchronizes to ∠M, ∠C corresponds to ∠N. And also if △ABC ≅ △LMN, then as per the CPCTC theorem, the matching sides and angles are equal, i.e. Abdominal muscle = LM, BC = MN, AC = LN, and ∠ A = ∠L, ∠B = ∠M, ∠C = ∠N.

CPCTC Triangle Congruence

CPCTC says that if two triangles are congruent by any criterion, then all the corresponding sides and also angles room equal. Here, us are pointing out 5 congruence criteria in triangles.

CriterionExplanationCPCTC
SSSAll the 3 corresponding sides are equalAll the equivalent angles are likewise equal
AAS2 corresponding angles and also the non had side room equalThe other equivalent angles and the other 2 equivalent sides are additionally equal
SAS2 equivalent sides and the contained angle are equalThe other matching sides and the various other 2 equivalent angles are also equal
ASA2 corresponding angles and also the contained sides are equalThe other equivalent angles and the various other 2 corresponding sides are also equal
RHS / HLThe hypotenuse and one leg of one triangle space equal to the equivalent hypotenuse and also a leg of the otherThe other matching legs and also the other two equivalent angles are equal

CPCTC Proof

To prove CPCTC, first, we should prove the the two triangles room congruent with the help of any type of one that the triangle congruence criteria. For example, take into consideration triangles ABC and CDE in i beg your pardon BC = CD and AC = CD room given.

Follow the points come prove CPCTC

BC = CD and also AC = CD (Given)Thus, △ABC ≅ △EDC; by SAS (side-angle-side) criterionNow the two triangles room congruent, therefore, making use of CPCTC, abdominal = DE, ∠ABC = ∠EDC and also ∠BAC = ∠DEC.

Important Notes

Given listed below are some vital notes regarded CPCTC. Have a look!

Look because that the congruent triangles maintaining CPCTC in mind.Before making use of CPCTC, present that the 2 triangles room congruent.

Related posts on CPCTC

Check the end these interesting short articles to know an ext about CPCTC and also its associated topics.

Example 1: Observe the number given below and find the length of LM utilizing the CPCTC theorem, if the is given that △ EFG ≅ △LMN.

Solution: Given the △ EFG ≅ △LMN. So, we can apply the ASA congruence preeminence to that which claims that if two matching angles and the included side space equal in two triangles, climate the triangles will certainly be congruent. Here, 2 angles are offered which space 30 degrees and also 102 levels such that ∠EFG = ∠LMN and ∠FEG = ∠MLN. So, by using the CPCTC theorem we deserve to identify that FE and ML room the equivalent sides of two congruent triangle △ EFG and △LMN. Therefore, FE = ML. Hence, the size of side LM is 3 units.

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Example 2: Observe the number given below in which PR = RS and also QR is perpendicular come PS. Find y using the CPCTC theorem.

Solution: First let united state prove that △PQR ≅ △SQR,

PR = RS (given)QR = QR (common side)∠QRP = ∠QRS (as QR is perpendicular to PS)Therefore, △PQR ≅ △SQR (SAS criterion)PQ = QS ( by CPCTC)

Now as PQ = QS