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Basic Theorems of Triangles Sophomore Geometry By: Shannon Manzella Interior Angles Theorem • In a Triangle, the Interior Angles will always add to be 180° – The Interior Angles are the inside angles between adjacent sides of a rectilinear figure. Example A • Solve for angle . Base Angles Theorem • If the sides of a triangle are congruent ( like in an Isosceles triangle) then the angles opposite these sides are congruent. – Two angles are congruent if they have the value and size. Leg A Base Angle B Leg B Base Angle A Example B • Solve for angle . Example C • Solve for angle . The Midpoint Theorem • The segment joining the midpoints of two sides of a triangle is parallel to the third side and half as long as the third side. – The Midpoint of a line segment is the point that is halfway between the endpoints of the line segment. Example D Example E Cites • http://www.toxel.com/wpcontent/uploads/2012/12/meltedcrayon08.jp g • http://www.mathwarehouse.com/geometry/t riangles/ • http://www.basic-mathematics.com/baseangles-theorem.html • http://www.cliffsnotes.com/math/geometry/p olygons/the-midpoint-theorem