Q: Why doesn't CPCTC guarantee that triangles are equilateral?

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'corresponding parts of congruent triangles are congruent'

CPCTC is an acronym for the phrase 'corresponding parts of congruent triangles are congruent' It means that once we know that two triangles are congruent, we know that all corresponding sides and angles are congruent.

A quadrilateral is a parallelogram if one pair of opposite sides are equal and parallel Let ABCD be a quadrilateral in which ABCD and AB=CD, where means parallel to. Construct line AC and create triangles ABC and ADC. Now, in triangles ABC and ADC, AB=CD (given) AC = AC (common side) Angle BAC=Angle ACD (corresponding parts of corresponding triangles or CPCTC) Triangle ABC is congruent to triangle CDA by Side Angle Side Angle BCA =Angle DAC by CPCTC And since these are alternate angles, ADBC. Thus in the quadrilateral ABCD, ABCD and ADBC. We conclude ABCD is a parallelogram. var content_characters_counter = '1032';

A. KL = ST B. JK= RS E. K =S -2023

I will outline a way to prove it for you. I will also five a simple vector proof for those that have studied vectors. For the first proof, one can often cite some of these as known facts or refer to theorems in a text. 1. First show that a rhombus is a parallelogram 2. Next, using the above, show that diagonals of the rhombus divide it into 4 congruent triangles. 3. Last, use CPCTC and not that all 4 middle angles are congruent so that are 90 degrees. From this is is easy to say that the diagonals are perpendicular. Hints. to prove 1, use the fact that all 4 sides of the rhombus are congruent and then use SSS to find two congruent triangles. Then use CPCTC to show that the angles are the same and find a transversal. Look at same side interior angles cut by that transversal and say something about them being parallel. 2. Use SSS again and find 4 congruent triangles and look at the diagonals. I will help more by giving you another proof using vectors that is really much more straightforward. A rhombus is a quadrilateral with all sides having equal length. This means that if two vectors, a and b that form the corner of a rhombus, then the magnitude of a and b are equal The diagonals of the parallelogram are precisely a+b and a-b. Now look at the dot product of a+b and a-b and see that it is zero and remember that a dot product of zero means the vectors are perpendicular or orthogonal The first part is a pure synthetic geometry approach and if anyone need more help to finish that, just ask, The second part is a vector proof which is elegant because it is so simple.

Related questions

You can only use CPCTC after you prove the 2 triangles congruent.

You can prove that to triangles are congruent with SSS, then use CPCTC to prove that two corresponding angles of those triangles are congruent.

Once you have shown that two triangles are congruent you can use CPCTC (corresponding parts of congruent triangles are congruent) to show the congruence of the remaining sides and angles.

Corresponding parts of congruent triangles are congruent.

CPCTC represents Corresponding Parts of Congruent Triangles are Congruent. You would use this in Triangle Proofs.

CPCTC or congruent

Corresponding parts of congruent triangles are congruent.

'corresponding parts of congruent triangles are congruent'

CPCTC is an acronym for the phrase 'corresponding parts of congruent triangles are congruent' It means that once we know that two triangles are congruent, we know that all corresponding sides and angles are congruent.

congruent -Gieco53-

CPCT

In gemortry, CPCTC is the abbreviation of a therom involving congrugent triangles. CPCTC stands for Corresponding Parts of Congruent Triangles are Congruent. CPCTC states that if two or more triangles are proven congruent by: ASA, AAS, SSS, HL, or SAS, then all of their corresponding parts are congruent as well.Ifthen the following conditions are true:A related theorem is CPCFC, in which triangles is replaced with figures so that the theorem applies to any polygon or polyhedrogen.