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Geometry Ch10.3 #7-12

Question from Emilio,

In Geometry Chapter 10, Lesson 3, Set 1, Pblms 7 – 12, I don’t understand what they are trying to teach comparing Descartes to the Side-Splitter Theorem. What I am supposed to learn from this set of problems?




Do not get too caught up in the side-splitter to Descartes method.


But here is the main idea

In the first problem (#7) you see the PRODUCT of two number (sides of a rectangle) represented as AREA. So, visually I can teach you math and area by showing you how it works in a rectangle. (Kind of like you might have learned area when you were younger – counting squares – and from that learned to multiply 2 x 3)

In the later problems, he is showing that you can ALSO show the product of two numbers as related to the lengths of parts of a triangle. This is just another (less obvious) visual/geometric method of showing a product.

What are you to take from this? Nothing except to recognize both are showing you geometrical ways we can represent the simple idea

c = ab.