EMAT 6690

Day 3 Equilateral Triangles ... Isosceles Triangles ... Constructions

Equilateral Triangles

An equilateral triangle is a three sided polygon that has all three angles that are equal in measure and all three sides that are congruent. An equilateral triangle is an equiangular triangle and also a regular triangle.

Each angle of an equilateral triangle measures 60 degrees.

Equilateral Triangle Construction

Start with segment AB and construct a circle with its center at point A and its radius congruent to AB. Now construct a circle with its center at point B and its radius congruent to AB. The intersection of the two constructed circles, point C, is the third vertex of our equilateral triangle.

Isosceles Triangles

An isosceles triangle is a triangle with at least two sides congruent. The congruent sides are called legs. The angles opposite the legs are base angles. The angle formed by two legs is the vertex angle. The third side is the base.

If two sides of a triangle are congruent, then the angles opposite those sides are congruent.

If two angles of a triangle are congruent, then the sides opposite those angles are congruent.

Equilateral Triangle Construction

Start with segment AB and a point D located so angle BAD is an acute angle. Construct a ray AD. Construct a circle with its center at point A and its radius congruent to AB. Point C is the intersection of the constructed circle and ray AD. Segment BC is the base of the isosceles triangle ABC. Segment AB and AC are the legs of isosceles triangle ABC.