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Relationships Within Triangles

Relationships Within Triangles. By Alex H., Brendon R., Caity C. 5-1 Midsegments of Triangles. Use midpoint formula, MP= , to determine where the segments will connect. A midsegment of a triangle is a segment connecting the midpoints of 2 sides. ( x1+x2 , y1+y2 ). 2 2.

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Relationships Within Triangles

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  1. Relationships Within Triangles By Alex H., Brendon R., Caity C.

  2. 5-1Midsegments of Triangles Use midpoint formula, MP= , to determine where the segments will connect A midsegment of a triangle is a segment connecting the midpoints of 2 sides ( x1+x2, y1+y2) 2 2

  3. 5-2Bisectors in Triangles There are 4 main types of bisectors: medians, altitudes, angle bisectors, & perpendicular bisector.

  4. The centroid is the point where the 3 medians all meet. The incenter is the point where the 3 angle bisectors all meet. CICOPAMA The circumcenter is the point where the 3 perpendicular bisectors all meet. The orthocenter is the point where the 3 altitudes all meet.

  5. Theorems Midsegment Theorem: The midsegment is parallel to the 3rd side & is ½ it’s length. Perpendicular Bisector Theorem: A point on the perpendicular bisector is equidistant from the endpoints of the segment. Angle Bisector Theorem: A point on the angle bisector is equidistant from the sides of an angle. The perpendicular bisectors of the sides of a triangle are concurrent at a point equidistant from the vertices. The bisectors of the angles of a triangle are concurrent at a point equidistant from the sides. the medians of a triangle are concurrent at a point that’s 2/3 the distance from each vertex to the midpoint of the opposite side. The lines that contain the altitudes of a triangle are concurrent. If 2 sides of a triangle aren’t congruent, then the larger angle lies opposite of the longer side. If 2 angles of a triangle aren’t congruent, then the longer side lies opposite of the larger angle. The sum of the lengths of any 2 sides must be greater than the length of the 3rd side.

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