1. Triangle Sum Theorem In a triangle, the three angles always add to 180°: A + B + C = 180° 38° + 85° + C = 180° 123 + C = 180° C = 57°

2. Isosceles Triangle Theorem A triangle with two congruent sides. The angles opposite the two equal sides are also congruent. 65  50 

3. Segments in Triangles The mid-segment of a triangle (also called a midline) is a segment joining the midpoints of two sides of a triangle. Properties: The mid-segment of a triangle joins the midpoints of two sides of a triangle such that it is parallel to the third side of the triangle. The mid-segment of a triangle joins the midpoints of two sides of a triangle such that its length is half the length of the third side of the triangle. Given DE is the length of the mid-segment. Find AB. Solution: The mid-segment is half of the third side. 7 is half of 14. AB = 14.

4. Medians The three medians of a triangle are concurrent and the concurrent point is called the CENTROID of the triangle. The centroid of a triangle divides the medians in the ratio 2:1, i.e. the length of the median from the vertex to the centroid is twice the length of the median from the centroid to the opposite side of the vertex.