Triangles

Triangles

1. Classifying Based on Sides

   • Scalene
     • No sides are equal
   • Equilateral
     • All sides are equal
   • Isosceles
     • Two sides are equal

2. Classifying Based on Angles

   • Obtuse
     • Angle above 90 degrees
   • Right
     • Angles that are 90 degrees
   • Acute
     • Angles below 90 degrees

3. Interior Angles

   • Sum equals 180 degrees
   • How to Get a Missing Angle
     • Step One
       • Add up the provided angle measurements
     • Step Two
       • Subtract that number from 180
     • Step Three
       • That number is the missing angle measurement

4. Triangle Congruency

   • When angles are congruent, they will have the same number of lines marking the angle
     • For example, two acute angles have 2 lines on each of the angles, these angles are congruent
   • When sides are congruent, they have the same number of dashes
     • For example, a triangle has a side with one dash, and the last two have two dashes, two of the sides are congruent

5. SSS, SAS, ASA, and AAS Congruency

   • SSS- When all sides are congruent
   • SAS- When two sides and an angle are congruent, but the angle is located in between the sides
   • ASA- When two angles and a side are congruent, but the side is in between the two angles
   • AAS- When two angles and a side are congruent, but the side is located on the outside of the congruent angles

6. Right Triangle Congruence

   • HL- Two right triangles are congruent if the hypotenuse and one corresponding leg are equal in both triangles.
   • LL- Two right triangles are congruent if one corresponding leg are equal in both triangles.
   • HA- Two right triangles are congruent if the hypotenuse and a corresponding angle are equal in both triangles.

7. Exterior Angle Theorem

   • The measure of an exterior angle of a triangle is greater than either of the measures of the remote interior angles.

8. Base Angles Congruence (Isosceles)

   • If two sides of a triangle are congruent, the angles opposite them are congruent

9. Mid Segment Theorem

   • In a triangle, the segment joining the midpoints of any two sides will be parallel to the third side and half its length

10. Side Splitter Theorem/Proportions

    • Theorem- If a line intersects two sides of a triangle and is parallel to the third side of the triangle, it divides those two sides proportionally
    • Proportions- Stating the ratios as fractions, setting the two fractions equal to each other, cross-multiplying, and solving the resulting equation