Adapted from Walch Education

Triangles A triangle is a polygon with three sides and three angles. There are many types of triangles that can be constructed. Triangles are classified based on their angle measure and the measure of their sides. Equilateral triangles are triangles with all three sides equal in length. The measure of each angle of an equilateral triangle is 60˚ : Constructing Equilateral Triangles Inscribed in Circles2

Circles A circle is the set of all points that are equidistant from a reference point, the center. The set of points forms a two-dimensional curve that is 360˚. Circles are named by their center. For example, if a circle has a center point, G, the circle is named circle G : Constructing Equilateral Triangles Inscribed in Circles3

Circles, continued The diameter of a circle is a straight line that goes through the center of a circle and connects two points on the circle. It is twice the radius. The radius of a circle is a line segment that runs from the center of a circle to a point on the circle. The radius of a circle is one-half the length of the diameter. There are 360˚ in every circle : Constructing Equilateral Triangles Inscribed in Circles4

Inscribing Figures To inscribe means to draw a figure within another figure so that every vertex of the enclosed figure touches the outside figure. A figure inscribed within a circle is a figure drawn within a circle so that every vertex of the figure touches the circle : Constructing Equilateral Triangles Inscribed in Circles5

6 Method 1: Constructing an Equilateral Triangle Inscribed in a Circle Using a Compass 1.To construct an equilateral triangle inscribed in a circle, first mark the location of the center point of the circle. Label the point X. 2.Construct a circle with the sharp point of the compass on the center point. 3.Label a point on the circle point A. 4.Without changing the compass setting, put the sharp point of the compass on A and draw an arc to intersect the circle at two points. Label the points B and C. 5.Use a straightedge to construct. 6.Put the sharp point of the compass on point B. Open the compass until it extends to the length of. Draw another arc that intersects the circle. Label the point D. 7.Use a straightedge to construct and.

1.3.1: Constructing Equilateral Triangles Inscribed in Circles7 Method 2: Constructing an Equilateral Triangle Inscribed in a Circle Using a Compass 1.To construct an equilateral triangle inscribed in a circle, first mark the location of the center point of the circle. Label the point X. 2.Construct a circle with the sharp point of the compass on the center point. 3.Label a point on the circle point A. 4.Without changing the compass setting, put the sharp point of the compass on A and draw an arc to intersect the circle at one point. Label the point of intersection B. (continued) 5.Put the sharp point of the compass on point B and draw an arc to intersect the circle at one point. Label the point of intersection C. 6.Continue around the circle, labeling points D, E, and F. Be sure not to change the compass setting. 7.Use a straightedge to connect A and C, C and E, and E and A.

Ms. Dambreville