length (stick)
shadow (stick)=
length (person)
shadow (person)length (stick)
length (person)=
shadow (stick)
shadow (person)Nonetheless, the units are still the same in each ratio. The first proportion uses length and shadow as units while the
second uses stick and person.
Similar Polygons
Pacing:This lesson should take one class period
Goal:This lesson connects the properties of proportions to similar polygons. An introduction to scale factors is also
presented within this lesson.
An alternative way of determining a scale factor is by using the fractionpreimageimage.This relates to the notion that similar
figures are formed by an applying an isometry, mapping an image onto its preimage. The first figure written in the
similarity statement represents the preimage and the second figure represents its corresponding image. Therefore,
the scale factork, is a ratio of the length of the image to the preimage.
Extension! A golden rectangle is a rectangle in which the ratio of the length to the width is the Golden Ratio,
approximately 1. 6180339888 .The Golden Ratio is denoted by the Greek letter Phi and can be found in nature,
biology, art, and architecture. For example, golden rectangles can be found all over the Parthenon in Athens, Greece.
Using the diagram below, have your students measure distances and find how many golden rectangles can be found.
http://www.geom.uiuc.edu/ demo5337/s97b/art.htm
Similarity by AA
Pacing:This lesson should take one class period
1.7. Similarity