Question

Explain congruence


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Answer 1

Answer:

In geometry, two figures or objects are congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the other.[1]

An example of congruence. The two triangles on the left are congruent, while the third is similar to them. The last triangle is neither congruent nor similar to any of the others. Congruence permits alteration of some properties, such as location and orientation, but leaves others unchanged, like distances and angles. The unchanged properties are called invariants.

More formally, two sets of points are called congruent if, and only if, one can be transformed into the other by an isometry, i.e., a combination of rigid motions, namely a translation, a rotation, and a reflection. This means that either object can be repositioned and reflected (but not resized) so as to coincide precisely with the other object. So two distinct plane figures on a piece of paper are congruent if we can cut them out and then match them up completely. Turning the paper over is permitted.

Answer 2

Answer:

The same shape and size, but we are allowed to flip, slide or turn. In this example the shapes are congruent (you only need to flip one over and move it a little). Angles are congruent when they are the same size (in degrees or radians). Sides are congruent when they are the same length. Congruent.

Step-by-step explanation:

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