Finals

• • When finding the measures of sides and angles in triangles, the longest side corresponds with the biggest angle, and the shortest side corresponds with the smallest angle.

  
• How to find out if three sides are able to create a triangle. add two sides and see if it is bigger than the side by itself. Keep repeating for every possibility. If at least two sides are not greater than the other side, the triangle can't be made. (i.e. side4+2 ≯ 7)
• • To find the segment of a median that starts at a point on a triangle and ends at the center, you can find it by taking two-thirds of the whole median.
  • To find the segment of a median that starts at one side of a triangle and ends at the center, you can find it by taking one-third of the whole median.
• A regular polygon has equal sides and equal interior angles
• The Inscribed Angle Theorem states that the measure of an inscribed angle is half the measure of the central angle that subtends it.
• • The orthocenter of a triangle is the intersection of its altitudes.
  • The incenter of a triangle is the intersection of its angle bisectors.
  • The circumcenter of a triangle is the intersection of its perpendicular bisectors.
  • The centroid of a triangle is the intersection of its medians.
• median of a triangle


  the segment that starts at one point and splits the opposite segment in half, making the the two split sides congruent (shown in the picture).

  
• altitude of a triangle


  a segment that starts at a point and intersects the side opposite of the point at 90 degrees (perpendicular).

  
• angle bisector of a triangle


  a segment that splits an angle at a vertex into half, making them congruent. The segments from the incenter to the side are congruent since they make up the radii of a circle (shown on picture).

  
• perpendicular bisector of a triangle


  A line segment that is perpendicular to a side and meets at the side's midpoint makes the side split into two congruent segments.

  
• perpendicular bisector of Isosceles triangle

  If this segment is in an isosceles triangle:

  • The angle where the two congruent sides meet is split into two and becomes congruent.
  • The base of the isosceles triangle is intersected at 90 degrees (perpendicular) and split into two congruent segments.