Triangles

Triangles

1. 3 sides

2. 3 vertices

3. Categorize based on side lengths

   • Right triangles
     • a triangle with a right angle.
   • Obtuse triangles
     • a triangle with one obtuse angle (greater than 90°)
   • acute triangles
     • A triangle with all three angles acute (less than 90 degrees)

4. Right triangle Congruency 10.24.16

   • Hypotenuse Leg Theorem
     • "if the hypotenuse and one leg of a right triangle are equal to the hypotenuse and one leg of another right triangle, then the two right triangles are congruent."
   • HL Right triangle congruence theorem: if the hypotenuse and a leg of a right triangle are congruent to another's right triangle hypotenuse and leg then the triangles are congruent.
   • LL right triangle congruence theorem: If the legs of one right triangle are congruent to the legs of another right triangle, then the two right triangles are congruent
   • LA right triangle Angle Theorem: If a leg and an acute angle of one right triangle are congruent to the corresponding parts of another right triangle, then the two right triangles are congruent.
   • (HA) Angle right triangle Theorem: If the hypotenuse and an acute angle of a right triangle are congruent to the hypotenuse and an acute angle of another right triangle, then the two triangles are congruent.

5. Base Angles Congruent (Isosceles) 10.25.16

   • If two sides of a triangle are congruent, then the angles opposite those sides are congruent.

6. Triangle Mid Segment Theorem 10.26.16

   • mid segment
     • half the length of the base
     • parrellel to the base

7. Proportions/ Side Splitter 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.
   • cross mulitply to solve
   • If a line is parallel to a side of a triangle and intersects the other two sides, then this line divides those two sides proportionally.