A student asks what's the difference between congruent and equals? ?

Question

A student asks what's the difference between congruent and equals? Give an example of two things that may be congruent, and two things that are equal.

Answer 1

In geometry congruent means that the figures have the same size and shape, the corresponding parts being equal each to each.

Examples:

1. Two equilateral triangles whose areas equal are congruent regardless of their orientation.

2. A 4" x 8" rectangle with its long side horizontal is congruent to an 8" x 4" rectangle wtih its short side inclined 45 degrees.

Equal means the two figures or quantities are identical.

Examples:

1. The area of a right triangle with 2" x 8" legs is equal to the area of a right triangle with 1" x 16" legs. The equality here refers to the areas. The given triangles however are not congruent.

2. A 12 inch diameter circle is equal only to another 12 inch diameter circle.The given figures are said to be identical. The given circles are also congruent.

Answer 2

Congruence usually involves geometric shapes, such as triangle ABC is congruent to triangle DEF, meaning their angle and side measures are the same.  Equals is used for mathematical equations, such as 2x = 4.

Answer 3

two triangles are congruent because the length of their corresponding sides are equal.