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# How do I use congruent triangles to provide proofs?

By Kris Boulton on the 11th of June, 2012

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Always remember that congruent triangles have congruent sides and angles.  A good pneumonic is Congruent Parts of Congruent Triangles are Congruent (CPCTC).  This means if triangle ABC is congruent to DEF, side A is equal to side D, side B to side E, etc.  Also, angle A is equal to angle D, etc.  This is important for geometric proofs

By brian on the 16th of January, 2013

## Use congruent triangles to solve problems and to provide proofs

Two shapes are congruent if they are completely the same. Their orientation or position can be different (in other words, they can be rotated, or moved around a grid), but all of their angles must be the same size, and sides the same length.

If any of these apply to two triangles, then we can prove that they are congruent:

SSS - Side Side Side - All 3 sides in both triangles are the same

SAS - Side Angle Side - 2 sides and the angle between them, are the same

AAS - Angle Angle Side - 2 angles are the same, and the same side in both traingles are the same

RHS - Right-angle Hypotenuse Side - In a right angle triangle, the hypotenuse and another side is the same

It is possible to use knowledge that two shapes are congruent to solve geometric problems.

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