a What types of parallelograms have all congruent sides?
B
b Of the parallelograms in Part A, which does not need any extra properties to describe it?
C
c Gather all information of types of parallelograms.
A
a Squares and rhombi
B
b Rhombus, see solution.
C
c
Practice makes perfect
a We are asked to name the types of parallelograms that have four congruent sides. Let's recall that a parallelogram is a quadrilateral with both pairs of opposite sides parallel. We will list all special types of parallelograms we know.
Looking at the above list, we can see that squares and rhombi have four congruent sides.
b In this part we want to determine what is the most precise name for the figure based only on the given description. To do this, let's recall the definitions of a square and a rhombus.
Square
A parallelogram with four congruent sides and four right angles.
Rhombus
A parallelogram with four congruent sides.
As we can see, based only on the given description the most precise name will be a rhombus since we do not have any information about angle measures.
c We will make a diagram for parallelograms such that at the top we place the most general term. The most general term is quadrilateral.
As we recalled, rectangles, rhombuses, and squares are all parallelograms. Therefore, this will be our second term.
Now, notice that a rhombus has four congruent sides while a rectangle has four right angles. Thus, these two terms are not related. Then, we place them at the same level next to each other.
Finally, we know that a square is both a rectangle and a rhombus. Then, we will place it at the bottom of our diagram with the corresponding arrows coming from rhombus and rectangle.
This diagram categorizes parallelograms from general to specific.
