a Follow the instructions you are given in the book.
B
b Use a protractor to measure the given angles you drew in Part A.
C
c What can you say about the angles you measured looking at the table you made in Part B?
A
a See solution.
B
b See solution.
C
c The diagonals of a parallelogram with four congruent sides intersect at right angles.
Practice makes perfect
a Let's start with drawing three parallelograms with all four sides congruent. To do this, we will draw a pair of segments of the same length with one common vertex.
Next we can use two rulers to get opposite sides parallel to each other. One of the rulers will be held still on a piece of paper and the other one will be moved along the first to get parallel lines. Let's move the horizontal ruler up along the ruler on the side. Next, we will draw another segment that has a length of 4, like the first one.
Now, we will connect two endpoints of the horizontal segments to get the fourth side. Notice that this side will also have the same length as the others.
We can draw the next two parallelograms, MNOP and WXYZ, in the same way. Try to have three varying figures.
Next, we are asked to draw the two diagonals for each figure. To do this, let's connect opposite vertices and name the point of intersection R.
b In this part, we are asked to measure the appropriate angles using a protractor. Let's start with the parallelogram ABCD and finding the measure of ∠ARB and ∠BRC.
We will measure the rest of the angles in the same way.
Now, as we know the measures of the appropriate angles, we can complete the given table.
Parallelogram
ABCD
MNOP
WXYZ
Angle
∠ARB
∠BRC
∠MRN
∠NRO
∠WRX
∠XRY
Angle measure
90
90
90
90
90
90
c As we can see from the table we made in Part B, all angles have a measure of 90. Therefore, we can assume that the diagonals of a parallelogram with four congruent sides intersect at right angles.
