MA.7.A.1.3 Solve problems involving similar figures. Block 28.
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MA.7.A.1.3Solve problems involving similar figures
Similarity is the basis of all measurement. It reveals the secret of map making and scale drawings. Similarity helps explain why a hummingbird's heart beats so much faster than a human heart, and why it is impossible for a small creature such as a praying mantis to become as large as a horse.
Do we really understand the definition of similarity?
Completing the enlargement
Proportional and Non-proportional relationships
Open the GeoGebra file
As you change the scale factor, notice the changes in Fig B
The point “Perimeter” moves in the coordinate system as the scale factor changes, what path does it describe?
Check the box perimeter to verify your conjecture as you change the scale factor
Is the relationship linear (proportional)? If yes, what is the equation of the line? What does the slope represent?
Do the same for the point “Area”
With the following activity we will explore some of these answers.
In the problem with squares, students could choose among three appropriate solution strategies:
(2) calculating and comparing the areas of both figures by means of the area formula
(3) applying the general principle ‘if length is increased by r, then area is increased by r2’.