Angle Bisectors

Angle bisectors are fundamental elements in geometry, serving to divide an angle into two congruent parts. They intersect the angle at its vertex, splitting it into two equal angles. Crucial in various geometric constructions and theorems, angle bisectors play a pivotal role in determining properties of triangles, such as the location of the incenter and the angle bisector theorem. Understanding their principles is essential for grasping geometric concepts and solving related problems efficiently. With their significance extending beyond basic geometry, angle bisectors are foundational components in mathematics education and practical applications in fields like architecture and engineering.

Questions
  • In triangle ABC, AD and BE are altitudes and AP and BQ are angle bisectors at A and B respectively, where P lies on CD and Q lies on CE. If #angle# PAD = 6° and #angle#QBE =18° , what is the degree of #angle#BCA?
  • Find the locus of a point equidistant from two lines #y=sqrt3x# and #y=1/sqrt3x#?
  • In an Isoceles #triangle# #ABC#,bisector #CD# of the #angle# #C# is equal to the base #BC#.Then the angle between #CDA# is ?
  • What is the incenter of a triangle?
  • Is the sum of measures of the angles of any triangle 90?