how do we use the exterior angle theorem?

To use the exterior angle theorem we have to understand what is an exterior angel is
 Exterior Angel -  triangle is equal to the sum of the measures of the two non-adjacent interior angles of the triangle.

The exterior angle theorem is that the exterior angle is the sum the two opposite angle.

for example say <b 60° and <a is 60° the sum of both those angles will equal <d making it 120° this means that <c is 60° (180°-120°= 60°)

for more help or other examples check out these links below:

• http://hotmath.com/hotmath_help/topics/exterior-angle-theorem.html
• http://www.regentsprep.org/Regents/math/geometry/GP5/LExtAng.htm
• http://www.youtube.com/watch?v=YS2K2SpvVIA
• http://classroom.westsidehsfaculty.org/webs/jschroe1/upload/worksheet_triangle_sum_and_exterior_angle.pdf
• http://www.kutasoftware.com/FreeWorksheets/GeoWorksheets/4-The%20Exterior%20Angle%20Theorem.pdf

What are the special angel we can create with parallel lines ?

What are the special angel we can create with parallel lines ?
Parallel Lines Are lines that never intersect and have the same slope.

 With these lines we can make angle out of them like: Transversal, Corresponding Angel, Alternate Exterior Angle ,Alternative Interior Angel

  
Transversal - A line that intersects two or more other coplanar line

Corresponding Angel - Angel that are in the same position relative to the transversal and line

 Alternate Exterior Angle - If two parallel like are cut by a transversal  then alternate interior angles are equal

  
Alternate interior angels - If two parallel like are cut by a transversal then alternate exterior angles are equal

    
For more help check out the links below  

• https://www.youtube.com/watch?v=Vvrac2aG6Y4&feature=related
• http://www.sparknotes.com/math/geometry1/constructions/section3.rhtml

How do we use the special segments in triangles?

Special Segment In Triangles have three main uses Median, Altitude & Angle Bisector 

• MEDIAN
  - The vertex often angle to the midpoint of the opposite side.
     EX ://  Line1 will go from point C to the middle of A&B (D)
  
• ALTITUDE
   - The height of a triangle meets the "ground" at a right angle.
• ANGLE BISECTOR
  - Bisects on angle in half creating two congruent angles.
    EX :// Line 1 goes from point A1 to T1  both sides are congruent to each other

For more help check these links 

• http://oxfordhsmath.weebly.com/uploads/8/6/0/3/8603550/lesson_11.pdf
• http://www.cliffsnotes.com/study_guide/Proportional-Parts-of-Triangles.topicArticleId-18851,articleId-18813.html 
• http://www.nelson.com/school/elementary/mathK8/quebec/0176237879/documents/NM8SB_10A.pdf 
• http://www.youtube.com/watch?v=imKupbXQ18I 
• http://www.youtube.com/watch?v=Uruz_XurwiQ&feature=fvwrel