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# Chapter 5

### Relationships within Triangles

Midpoint Formula (x1+x2/2,y1+y2/2)
Distance Formula Square Root of 9(x1-x2)2+(y1-y2)2
Slope Formula y2-y1/x2-x1
Midsegment Theorem the midsegment of a triangle is parallel to the third side and is half as long as the third side
Perpendicular Bisector Theorem in a plane, if a point is on the perpendicular bisector of a segment, the the point is equidstant from the end points of the segment
Converse of the Perpendicular Bisector Theorem in a plane, if a point is equidstant from the end points of the segment, then the point is on the perpendicular bisector of a segment
Angle Bisector Theorem if a point on the bisector of an angle, then the perpendicular segments from the point to each ray
Converse Angle Bisector Theorem if a point is in the interior of an angle and the perpendicular segments from the point to each ray are equidstant, then it lies on the bisector of the angle
Incenter of a Triangle Theorem the incenter of a triangle is equidstant from the sides od the triangle
Concurrency of Medians of a Triangle Theorem the centroid is 2/3 of the distance from each vertex to the midpoint of the opposite side
Parts of an Isosceles Triangle in an isoscels triangle, if an altitude, median, perpendicular bisector, and angle bisector comes from the vertex angle, then that segment is also an altitude, median, perpendicular bisector, and angle bisector.
Side Theorem if 1 side of a triangle is longer than another side, then the angle opposite the longer side is larger than the angle opposite the shorter side
Angle Theorem if 1 angle of a triangle is longer than another angle, then the side opposite the larger angel is longer than the side opposite the smaller angle
Triangle Inequality Theorem the sum of the lengths of any 2 sides of a triangle is greater than the length of the 3rd side
Hinge Theorem if 2 sides of 1 triangle are congruent to 2 sides of another triangle and the included angle of the 1st is larger than the included angle of the 2nd, then the 3rd side of the 1st is longer than the 3rd side of the 2nd
Converse of the Hinge Theorem if 2 sides of 1 triangle are congruent to 2 sides of another triangle and the 3rd side of the 1st is longer than the 3rd side of the 2nd, then the included angle of the 1st is larger than the included angle of the 2nd
Created by: nhpride