using the law of detachment, what can be concluded regarding the following statements: If a figure is a rhombus, then it is an eqilateral quadrilateral. A square is a rhombus.

a) a rhombus is a square
b) a square is a rhombus
c) a square is an equilateral quadrilateral
d) an equilateral quadrilateral is a square

A square is a rhombus, but a rhombus isn't neccessarily a square.

The ans. = b.

Why isn't it also c?

To use the law of detachment, we need two statements: a conditional statement (if-then statement) and the hypothesis of that conditional statement being true. The law of detachment allows us to conclude the conclusion of the conditional statement if the hypothesis is true.

Let's break down the statements given:

Statement 1: If a figure is a rhombus, then it is an equilateral quadrilateral.
This is a conditional statement in the form "if A, then B." The hypothesis (A) is "a figure is a rhombus," and the conclusion (B) is "it is an equilateral quadrilateral."

Statement 2: A square is a rhombus.
This statement tells us that a square is a specific type of figure that falls under the category of a rhombus.

Now, let's apply the law of detachment:

Step 1: Identify the hypothesis from statement 1.
The hypothesis from statement 1 is "a figure is a rhombus."

Step 2: Compare the hypothesis from statement 1 to statement 2.
We see that statement 2 states that "a square is a rhombus," which matches the hypothesis from statement 1.

Step 3: Apply the law of detachment.
According to the law of detachment, if a figure is a rhombus (hypothesis from statement 1) and we know that a square is a rhombus (statement 2), we can conclude that a square is an equilateral quadrilateral.

Therefore, the correct conclusion using the law of detachment is:
c) a square is an equilateral quadrilateral.