TRIANGLES

TRIANGLES

1. LESSON 4-1

   • CLASSYFING BY ANGLES
     • angles
     • sides
     • acute
       • 3 acute angles
     • equiangular
       • 3 congruentemente acute anglesl
     • obtuse
       • 1 obtuve angle
     • right
       • 1 riget angle
   • CLASSIFYING BY SIDES
     • Equilateral
       • 3 congruentemente sides
     • Isosceles
       • at least 2 congruentemente sides
     • Scalene
       • no congruente sides

2. LESSON 4-3

   • congruente and corresponding parts
     • when they have th same shape and size
   • provino Triangles congruency
     • if 2 angles of one triangle are congruente to the 2 angles of the other Triangles then the 3rd angle of both triangles are congruent

3. LESSON 4-2

   • angle- sum theorem
     • the sum of the Measure of the angles
   • exterior angle theorem
     • the measurment of an exterior anuléis equal to the sum of the measurments of the two remote interior angles

4. LESSON 4-4

   • Side - Side - Side
     • If 3 sides of one Triangles are congruent to 3 sides of a Second Triangles, then the Triangles are congruent
   • Angle- side- angle
     • If 2 sides and the included angle of one Triangles are congruent to 2 sides and the included angle of a Second Triangles, then the Triangles are congruent

5. LESSON 4-5

   • Included side
     • is the side located between two consecutivo angles of a polygon
   • angle- side -angle
     • if 2 angles and the included side of one Triangles are congruent to 2 angles and the included side of another triangle, then the Triangles are congruent
   • Angle- angle- side
     • if 2 angles and the nonincluded side of one Triangles are congruent to the corresponding 2 angles and side of a 2nd triangle, then the 2 triangle are congruent

6. LESSON 4-6

   • les of an iscoseles triangle
     • the 2 congruent sides
   • vertex angle
     • angle with sides that are the less is called
   • based angles
     • 2 angles formed by the base and the congruent sides
   • isósceles theorem
     • 2 sides of a triangle are congruent then the opposite those sides are congruent
   • isósceles converse theorem
     • If 2 sides of a triangle are congruent, then the angles opposite those sides are congruent

7. LESSON 5.1

   • perpendicular bisector theorem
     • If a Point is on the perpendicular bisector of a segmento, then its equidistante from the endpoints of a segment
   • Converse of the perpendicular bisector theorem
     • if a point is equidistance from the endpoints of a segment. then it is on the perpendicularbisector of the segment
   • converse of the perpendicular bisector theorem
     • if a point is equidistante of from he endpoints of a segment, then it is on the perpendicular bisector of the segment
   • circumcenter theorem
     • the perpendicular bisector of a triangle intesect at a point called the circumcenter that is equidistante from the vértices of the triangle
   • Angle bisector theorem
     • If a point is on the bisector angle, then it is quidistance from the sides of the angle
   • converse of the angle bisector theorem
     • if a point in the interior of an angle is equidistante from the sides of the angle, the it is on the bisector of the angle
   • in center theorem
     • the angle bisector if a triangle izntersect at a point called the incenter that is equidistante from the sides of the triangle.

8. LESSON 5.2

   • centroid theroem
     • the medias of a triangle interdecís at a point called the centroid that is 2 thirds of the distance from each verte to the midpoint of the opposite
   • orthocenter
     • the Lines containing the altitudes of a triangle are concurren, intersecting at a point called the orthocenter

9. LESSON 5.3

   • angle- side relationships in triangles
     • if one sides of a triangle is longer than the other side, then the angle opposite the longer side has a greater Measure then the angle opposite the shorter side
     • if one triangle has a greater Measure than another angle, then the side opposite the greater angle is longer than the side opposite the lesser angle

10. LESSON 5.5

    • triangle inequality theorem
      • the sum of the lenghts of any 2 sides of a triangle must be greater than the lenght of the 3rd side

11. LESSON 5.6

    • hinge theorem
      • if 2 sides of a triangle are congruent to 2 sides of another triangle, and included angle of the 1st triangle is larger than the included side of the 2nd triangle, then the 3rd side of the 1st triangle is longer than the 3rd side of the 2nd triangle
    • converse of the hinge theorem
      • if 2 sides of a triangle are congruent to the 2 sides of another triangle, and the 3rd side in the 2st longer than the 3rd side in the 2nd triangle, then the inccluded angle measure of the 1st triangle is greater than the included angle measure in the 2nd triangle.

12. LESSON 4-7

    • Transfomracion
      • is an operation that maps an original geométrico figure
    • Congruente transformacion
      • Is one in with the position of the image May differ from that of the preimage

13. MAYRA CHAVARRIA, 9-7