# im.g.1.14.3.Turning into Triangles

1. Draw a segment. Label the endpoints A and B.
1a. Rotate segment AB clockwise around center B by 90 degrees. Label the new endpoint A'.
1b. Use the Polygon tool to draw triangle ABA'.

1c. What kind of triangle did you draw? What properties do you notice in the figure. Explain your reasoning.

2. On the same grid, draw a segment. Label the endpoints C and D.
2a. Rotate segment CD counterclockwise around center D by 30 degrees. Label the new endpoint C'.
2b. Rotate segment C'D counterclockwise around center D by 30 degrees. Label the new endpoint C".
2c. Use the Polygon tool to draw triangle CDC".

2d. What kind of triangle did you draw? What other properties do you notice in the figure? Explain your reasoning.

3. You constructed an equilateral triangle by rotating a given segment around one of its endpoints by a specific angle measure. An equilateral triangle is an example of a regular polygon: a polygon with all sides congruent and all interior angles congruent. Try to construct some other regular polygons with this method. (Say, a square... or a regular pentagon. What would that angle of rotation be for a regular pentagon? How could you figure it out?)

## Attribution

Illustrative Mathematics, geometry, unit 1, lesson 14, activity 3,
Turning into triangles.

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