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We are asked to describe how algebraic concepts are applied to geometry. Before we do that, let's remember what these branches of mathematics are.
At first, these two areas of mathematics may seem unrelated. This is not true. To prove this point, we will describe three ways that algebra can be applied to geometry.
See that we took an algebraic object — an equation — and we graphed it. This made it a geometric object: a line.
We can use algebra in other ways. Consider any circle.
If we want to find its area, we substitute its radius r into the following formula and evaluate. A = π r^2 For example, this is the area of a circle with a radius of 4 units. A &= π ( 4)^2 & = 16π Notice that we calculated the area of the circle using an algebraic formula. The properties we used when simplifying the expression are also algebraic concepts.
In this chapter we learned about the Pythagorean Theorem. This theorem tells us about the relationship between the lengths of sides in a right triangle.
One of the ways we used this theorem was to solve a right triangle. This is another example of how an algebraic concept, in this case the Pythagorean Theorem, can be applied to geometry.
