Unit 2: Stretching and Shrinking
Essential Question: How can we analyze proportional relationships and use them to solve problems?
In this unit, we will find relationships among figures that have been stretched or shrunk. We will analyze the resulting changes in properties of the figures, such as area and perimter. Similarity will also be used to find the heights of real objects (such as buildings or flagpoles.)The problems are set up to have us begin to reason proportionally. By the end of the unit, you will know how to create similar figures, how to determine whether or not two figures are similar, and how to predict the ratios of the lengths and areas of two similar figures. The next unit will go deeper into proportional ideas.
Definition: polygons are similar if their corresponding (matching) angles are congruent (equal in measure) and the ratio of their corresponding sides are in proportion.
These triangles are similar because
1) all of the angles are equal
2) the corresponding sides are proportional
The scale factor is 2.
Each side of the smaller triangle is multiplied by 2 to create the larger triangle.