Triangles

Triangles

1. Classifying

   • By angles
     • Acute
       • 3 acute angles
     • Equiangular
       • 3 congruent acute angles
     • Obtuse
       • 1 obtuse angle
     • Right
       • 1 right angle
   • By sides
     • Equilateral
       • 3 congruent sides
     • Isosceles
       • 2 congruent sides
     • Scalene
       • no congruent sides
   • Isosceles
     • If 2 sides of a triangle are congruent the opposite angles are congruent
     • Converse
       • If 2 angles are congruent, then the opposite sides are congruent

2. Congruency

   • They're congruent if sides and angles are congruent
   • Proving they're congruent
     • SSS:
       • if 3 sides are congruent to 3 sides, then the triangles are congruent
     • SAS:
       • if 2 sides and included angle are congruent to 2 sides and included angle, then the triangles are congruent
     • ASA:
       • if 2 angles and included side are congruent to 2 angles and included side, then triangles are congruent
     • AAS:
       • if 2 angles and nonincluded side are congruent to 2 angles and nonicluded side, the triangles are congruent

3. Special Segments

   • !Medians & Altitudes
     • From vertex to midpoint of opposite side.
       • CENTROID- where they meet.
     • From vertex to opposite side perpendicular to that side.
       • ORTHOCENTER- where they meet
   • Perpendicular
     • Perpendicular to the segment and equidistant from the endpoints of the segment
       • CIRCUMCENTER- where they meet
   • Angle Bisector
     • Cuts the angles in half and it is equidistant from the sides of the angle
       • INCENTER- where they meet

4. Angles

   • Sum of measure of angles = 180
   • Exterior angle is the sum of measure of the 2 remote interior angles

5. Transformations

   • The position of the image may differ from the preimage but are still congruent
     • TYPES:
       • 1. Reflection- q flip over the line of reflection
       • 2. Translation: slide in same direction and distance
       • 3. Rotation: a turn around the center of rotation

6. Inequalities

   • One Triangle
     • exterior angles are the sum of its 2 remoteinterior angles
     • if one side is bigger that another, then it's opposite angle is bigger than the other
   • The Triangle Inequality
     • The sum of each 2 sides has to be bigger than the measure of the remaining side & viceversa
   • Two Triangles
     • 2 sides of 2 tringles are congruent but one angle is bigger, then you know that that side is bigger, & viceversa