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Illustrative Math
Grade 8
Let’s figure out if a triangle is a right triangle.
Illustrative Math Unit 8.8, Lesson 9 (printable worksheets)
The following diagram shows how to use the Converse of the Pythagorean Theorem to determine if a triangle is a right triangle.
Consider the tips of the hands of an analog clock that has an hour hand that is 3 centimeters long and a minute hand that is 4 centimeters long.
Over the course of a day:
Here are three triangles with two side lengths measuring 3 and 4 units, and the third side of unknown length.
Sort the following six numbers from smallest to largest. Put an equal sign between any you know to be equal. Be ready to explain your reasoning.
A similar argument also lets us distinguish acute from obtuse triangles using only their side lengths.
Decide if triangles with the following side lengths are acute, right, or obtuse. In right or obtuse triangles, identify which side length is opposite the right or obtuse angle.
a = 15, b = 20, c = 8
15^{2} + 8^{2} = 289
20^{2} = 400
400 > 289
Obtuse triangle. The side length opposite the obtuse angle is 20.
a = 8, b = 15, c = 13
8^{2} + 13^{2} = 283
15^{2} = 225
225 < 283
Acute triangle
a = 17, b = 8, c = 15
8^{2} + 15^{2} = 289
17^{2} = 289
289 = 289
Right triangle. The side length opposite the right angle is 17.
The Open Up Resources math curriculum is free to download from the Open Up Resources website and is also available from Illustrative Mathematics.
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