what is the difference between MS=DG and line MS=line DG

Question

what is the difference between MS=DG and line segment MS about eqauls line segment DG?

 

Answer 1

When you say "about equals," I have a feeling you actually mean "is congruent to."

This is an important concept in geometry: understanding the difference between being equal and being congruent.

Equality only refers to numbers, not objects.  For example, angles can have equal degrees, because degrees are numbers.  Line segments can have equal lengths, because lengths are measured in inches, feet, etc., all of which are numbers.  And I could simply say that 10 is equal to 10, because 10 is a number.

However, the congruent symbol (the equal sign with a ~ over it) refers to objects which have equal measures.  For example, two angles are congruent because they have the same number of degrees.  Your two line segments, MS and DG, are congruent if they have the same length.

So to summarize: in geometry, use an equal sign when you want to talk about degrees, length, or other numbers.  Use a congruent symbol when you want to describe objects such as angles, shapes, or line segments.

Here's a silly example that might help you remember.  Joe and John are identical twins.  They are the same height, which is a number, so that's the EQUAL part...their height.  Because all their "numbers" match up (their height, hand length, size of ears), we say they are identical twins (that's the CONGRUENT part).

It's a very technical difference, but one you will see quite often, especially if you're doing proofs.