Question

If a figure consists of 4 sides that are all congruent, then it is a parallelogram. Figure ABCD is a parallelogram. Therefore, ABCD has 4 congruent sides.

Determine if the statement is valid.

A.
No, 2004-01-03-05-00_files/i0190002.jpg, 2004-01-03-05-00_files/i0190000.jpg is an invalid argument.
B.
No, 2004-01-03-05-00_files/i0190002.jpg, 2004-01-03-05-00_files/i0190001.jpg is an invalid argument.
C.
Yes, 2004-01-03-05-00_files/i0190002.jpg is true, therefore 2004-01-03-05-00_files/i0190003.jpg is true. It is a valid argument.
D.
There is not enough information to determine.

Answer 1

A parallelogram is a flat shape with four sides. It's quadrilateral, meaning it has four sides, and parallel, or opposite, sides are equal.

Opposite angles are also equal.

Squares are parallelograms -- they have four sides, and opposite sides are equal to each other (in fact all four sides are equal, so opposite sides have to be equal).

Rectangles are parallelograms -- again, four sides, and opposite sides are equal to each other, although in this case, one pair is longer than the other.

Rhombuses are parallelograms -- they look like diamonds -- four sides, opposite sides and angles equal, and if you draw diagonal lines from point to point, they bisect each other at right angles.

Now what you're posing isn't so much a math concept as a logic concept. If/then. So here's what we know:

* A figure that has 4 congruent sides = parallelogram.
* Figure ABCD = parallelogram.
* ABCD = figure with 4 congruent sides.

Since it's expressed as an absolute (in other words, they didn't say "some figures with 4 congruent sides are parallelograms), then they're stating that ALL parallelograms have 4 congruent sides (they didn't say there aren't other shapes with 4 congruent sides, but they did say all parallelograms have them). They also say that ABCD is a parallelogram, and that parallelograms have 4 congruent sides, no exceptions listed. So in that case, ABCD, which is a parallelogram, must have 4 congruent sides, because it's a parallelogram and parallelograms do.