Isosceles Triangle Conjectures

1
Isosceles Triangle Conjectures

• In a scalene triangle, the median, angle
  bisector, and altitude are separate segments.
• In triangle ARC at right there are three
  segments
• altitude CD to the base AR,
• angle bisector CE of angle ACR, and
• median CF to the base AR
• What happens if this triangle becomes isosceles?
• http//www.keymath.com/DG/dynamic/page241.html

2
Isosceles Triangle Conjectures

• As demonstrated by the web investigation, the
  median, altitude, and angle bisector to the base
  of an isosceles triangle are the same segment.
• This can be proven using triangle congruence
  conjectures and CPCTC.
• This segment is called the Symmetry Line of an
  Isosceles Triangle
• An equilateral triangle has three such lines of
  symmetry

3
Isosceles Triangle Conjectures

• Prove that the bisector of the vertex angle of an
  isosceles triangle divides it into two congruent
  triangles.

4
Isosceles Triangle Conjectures

• C-28 Vertex Angle Bisector Conjecture
• In an isosceles triangle, the bisector of the
  vertex angle is also the median to the base and
  the altitude to the vertex.

5
Isosceles Triangle Conjectures

• C-28 Vertex Angle Bisector Conjecture
• In an isosceles triangle, the bisector of the
  vertex angle is also the median to the base and
  the altitude to the vertex.