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.
- Corollary 1–An equilateral triangle is also equiangular.
- Corollary 2–An equilateral triangle has three 60 degree angles.
- 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.
- 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.
Return to Triangles Main Page