TRIANGLES

TRIANGLES

1. Angles

   • Triangle Angle-Sum Theorem - The sum of the angles of a triangle is 180°.
   • Exterior Angle Theorem - The exterior angle is the sum of the two remote interior angles.

2. Congruence

   • Proving Triangle are Congruent
     • Side-Side-Side (SSS) Three pairs of corresponding sides are congruent.
     • Side-Angle-Side (SAS) Two pairs of corresponding sides and their included angles are congruent.
     • Angle-Side-Angle (ASA) Two pairs of corresponding angles and their included sides are congruent.
     • Angle-Angle-Side (AAS) Twi pairs of corresponding angles and the corresponding non included sides are congruent.
   • Congruent Triangles
     • Congruent Polygons= corresponding parts(side, angles) are congruent CPCTC---Corresponding Parts of Congruent Triangles are Congruent

3. Transformations

   • Reflection
   • Translation
   • Rotation

4. Special Segments

   • Altitudes and its Orthocenter
   • Medians and its Centroid
   • Angle Bisector and its Incenter
   • Perpendicular Bisector and its Circumcenter

5. Inequialities

   • Triangle Inequality Theorem - The sum of two sides of a triangle are greater than the third side of the triangle.
   • Inequalities on the Two Triangles
     • Hinge Theorem: If two sides of a triangle are congruent to the sides of the second triangle and the the included angles of the first triangle are greater than the second, then the third side of the first triangle is greater then the second triangle.
     • The converse of the Hinge Theorem: If two sides of a triangle are congruent to the sides of the second triangle and the third side in the first triangle is longer than the second, then the included angle measure is greater than the second.
   • Angle Side Realtioships in Triangles
     • The bigger the angle, the bigger the opposite side. The smallest the opposite side, the smallest the angle.

6. Classifying

   • Sides
     • Scalene Triangle
     • Isosceles Triangle
       • - The opposite angles of the congruent sides are congruent. - If two angles are congruent then the opposite sides are congruent.
     • Equilateral Triangle
       • - It is equilateral it in equiangular and all angles equal 60°.
   • Angles
     • Acute Triangle
     • Right Triangle
     • Equiangular Triangle
     • Obtuse Triangle

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