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A student cut a triangular shape out of blue construction paper and labeled the angles $\angle 1, \angle 2$ and $\angle 3,$ as shown in figure (a) below. Then she tore off each of the three corners and arranged them as shown in figure (b). Explain what important geometric concept this model illustrates.

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Chapter 9

An Introduction to Geometry

Section 3

Triangles

01:50

A student cut a triangular…

03:02

Draw a diagram and describ…

01:53

02:03

The key principle here is that in part a those air the three angles of a triangle and we know that the sum of the measures of the three angles of any triangle have to total 180 degrees if I rip those up and put them next to each other, the key idea for B is that they are now making a straight angle. So if I have a straight angle here, I know that measure is 180 degrees. So if I take the three angles and turn them facing the direction you have there and put them on a straight angle anyway, you do it. You would divide that, um, that section completely, because the the total would also be 180 degrees.

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