4.1 Ratios Within Similar Parallelograms
Name:_________________________________ Period:____
You can enhance a report or story by adding photographs,
drawings or diagrams. If you place a graphic in an electronic
document, you can enlarge, reduce or move it. When you
click on the graphic, it appears inside a frame with handles
along the sides, such as the figure to the right. You can
change the size and shape of the image by dragging the
handles.
Here are some examples after the image has been resized:
•
How did this technique produce variations of the original shape?
•
Which of these images appears to be similar to the original? Why?
You can use ratios to describe and compare shapes. A ratio is a comparison of two quantities, such as two lengths.
The rectangle around the original figure is about 10 cm tall and 8 cm wide. You can say, “The ratio of height to width
is 10 to 8.”
This table gives the ratios of height to width
for the images on the front page.
What do you notice about the height to width
ratios?
The comparisons “10 to 8” and “5 to 4” are equivalent ratios. Equivalent ratios are like equivalent fractions. In fact,
ratios are often written in fraction form. You can express equivalent ratios with equations. A proportion is an
ଵ଴ ହ
଼
ସ
equation stating that two ratios are equal.
=ସ
=
଼
ଵ଴ ହ
You know that scale factor relates each length in a figure to the corresponding length in its image. You can also
write a ratio to compare any two lengths in a single figure.
For the diagrams in this Investigation, all measurements are drawn to scale unless otherwise noted.
A. 1. Which rectangles are similar? EXPLAIN YOUR REASONING.
2. a. For each rectangle above, find the ratio of the length of the short side to the length of the long side.
4.1 Ratios Within Similar Parallelograms
Name:_________________________________ Period:____
2. b. What do you notice about the ratios in part (a) above for similar rectangles from #1?
What about the ratios for non-similar rectangles?
3. Choose two similar rectangles from the front. Find the scale factor from the smaller rectangle to the larger
rectangle. What does the scale factor tell you?
4. Compare the information you found from #3 above to the information you found with the ratios of the side
lengths from #2.a.
B. 1. Which of the parallelograms below are similar? EXPLAIN YOUR THINKING.
2. For each parallelogram, find the ratio of the length of the long side to the length of the short side. How do the
ratios compare?
C. 1. Suppose you find the ratios of the lengths of adjacent sides, two sides that meet at a vertex, in a rectangle. This
ratio is equivalent to the ratio of the corresponding side lengths in another rectangle. Are the figures similar?
EXPLAIN YOUR REASONING.
2. Suppose you find the ratio of the lengths of adjacent sides in a parallelogram. This ratio is equivalent to the ratio
of the adjacent sides in another parallelogram. Are the figures similar? EXPLAIN YOUR REASONING.