Congruency Theorems

Congruency Theorems

1. Side Side Side

   • two triangles, three sides are congruent to each other

2. Side Angle Side

   • two sides in a triangle and an angle are congruent to each other
     • *angle has to be in between of the sides*

3. Angle Side Angle

   • two angles and a side are congruent to each other

4. Angle Angle Angle

   • two angles and a side HAVE to be congruent

5. Right Triangle Congruency Theorem

   • 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

6. Exterior Angle Theorems

   • add the two degrees that are on the interior & use that as your exterior

7. Base Angle Congruent

   • if two sides of a triangle are congruent then the opposite angles are congruent
     • if two angles of a triangle are congruent then the opposite sides are congruent

8. Triangle Mid Segment Theorem

   • the mid-segment of a triangle is a segment joining the midpoints of two sides of a triangle

9. Side Splitter Theorem

   • if a line is parallel to a side of a triangle and intersect the other two sides, then this line divides those two sides proportionally
     • Proportions
       • two ratios (fractions) are equal
         • 1/3 = 2/6