Triangles Theorems Page

Triangle Theorems

  • SSS Postulate–If three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent.
  • SAS Postulate–If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent.
  • ASA Postulate–If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent.
  • Isosceles Triangle Theorem–If two sides are congruent, then the angles opposite those sides are congruent.
  1. Corollary 1–An equilateral triangle is also equiangular.
  2. Corollary 2–An equilateral triangle has three 60 degree angles.
  3. Corollary 3–The bisector of the vertex angle of an isosceles triangle is perpendicular to the base at its midpoint.
  • If two angles of a triangle are congruent, then the sides opposite those angles are congruent.
  1. Corollary–An equiangular triangle is also equilateral.
  • AAS Postulate–If two angles and a non-included side of one triangle are congruent to the corresponding parts of another triangle, then the triangles are congruent.
  • HL Postulate–If the hypotenuse and a leg of one right triangle are congruent to the corresponding parts of another right triangle, then the triangles are congruent.
  • If a point lies on the perpendicular bisector of a segment, then the point is equidistant from the endpoints of the segment.
  • If a point is equidistant from the endpoints of a segment, then the point lies on the perpendicular bisector of the segment.
  • If a point lies on the bisector of an angle, then the point is equidistant from the sides of the angle.
  • If a point is equidistant from the sides of an angle, then the point lies on the bisector of the angle.

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