a Follow the instructions you are given in the book.
B
b Use a ruler to measure diagonals of the rectangles you drew in Part A.
C
c What can you say about the diagonals of these rectangles looking at the table you made in Part B?
A
a See solution.
B
b See solution.
C
c The diagonals of a rectangle are congruent.
Practice makes perfect
a Let's start with drawing three pair of segments that are both congruent and parallel. To do this, we can use two rulers. 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 left side. Next, we will draw a segment that will also have a length of 4, as the first one. Remember that to get a rectangle, we need to start in the same place of the ruler.
Now, as we have one pair of parallel and congruent segments, we will connect the endpoints to form the first rectangle ABCD.
We can draw the next two rectangles, MNOP and WXYZ, in the same way. Try to have three varying figures.
Next, we are asked to draw the two diagonals for each rectangle. To do this, let's connect opposite vertices.
b Now we are asked to measure each diagonal, and complete the given table. To do this, we will use a ruler. Let's start with quadrilateral ABCD.
We will measure the rest of the diagonals in the same way.
Now, as we know the measures of the diagonals, we can complete the given table.
Rectangle
Side
Length
ABCD
AC
4.3
BD
4.3
MNOP
MO
3.6
NP
3.6
WXYZ
WY
7.3
XZ
7.3
c As we can see from the table we made in Part B, all three rectangles have diagonals of the same length. Therefore, we can assume that the diagonals of a rectangle are congruent.
