Must Know High School Geometry by Allen Ma

Author:Allen Ma
Language: eng
Format: epub
Publisher: McGraw-Hill Education
Published: 2019-04-15T00:00:00+00:00

Using the Distance Formula to Classify Shapes

Now that we know how to use the distance formula, let’s use it to show the special properties of the different triangles and parallelograms we learned about in previous chapters of this book. In Chapter 3 we learned how to classify triangles as isosceles, equilateral, and right using their side lengths. In Chapter 8 we learned how to classify quadrilaterals as parallelograms, squares, rhombuses, and rectangles using their side length. Because the distance formula finds the length between two points, we must be able to use it to classify these different figures if we are given the coordinates for the vertices of the figure. Let’s try this in the next example.

EXAMPLE

Consider ∆MAT with M(1,1), A(4,6), and T(7,11). Using coordinate geometry, prove that ∆MAT is an isosceles triangle.

One property of an isosceles triangle is that two of the sides are congruent. We can use the distance formula to find the lengths of the sides of the triangle and show that two sides have the same length. For visual purposes, don’t ever be afraid to plot the points on graph paper.

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