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Level 127

Postulates & Theorems for Triangles


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Exterior angle theorem
The measure of an exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles.
Third Angles Theorem
If 2 angles of one triangle are congruent to 2 angles of another then the third angles are also congruent
Side-Side-Side (SSS) Congruence Postulate
If three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent
Side-Angle-Side (SAS) Congruence Postulate
If two sides and the included angle of one triangle are congruent to two sides and the included angle of another
Angle-Side-Angle (ASA) Congruence Postulate
If two angles and the included side of one triangle are congruent to two angles and the included side of another
Angle-Angle-Side (AAS) Congruence Theorem
If two angles and a non-included side of one triangle and congruent to two angles and the corresponding non-included side of a second triangle, then the two triangles are congruent.
Hypotenuse-Leg (HL) Congruence Theorem
If the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and a leg of a second right triangle, then the two triangles are congruent.
Isosceles Triangle Theorem
If 2 sides of a triangle are congruent, then the angles opposite those sides are congruent
Converse of the Isosceles Triangle Theorem
If 2 angles of a triangle are congruent, then the sides opposite those angles are congruent.
Corollary 4-8-3
If a triangle is equilateral, then it is equiangular
Corollary 4-8-4
If a triangle is equiangular, then it is equilateral.
Exterior Angle Inequality
The measure of an exterior angle of a triangle is greater than the measure of either of the two remote interior
Perpendicular Bisector Theorem
if the perpendicular bisector goes through a vertex of a triangle the legs will be congruent
Converse of the Perpendicular Bisector Theorem
in a plane, if a point is equidistant from the endpoints of a segment, then it is on the perpendicular bisector of the segment
angle bisector theorem
if a point is on the bisector of an angle, then it is equidistant from the other two sides of the angle
Converse of the Angle Bisector Theorem
if a point is in the interior of an angle and is equidistant from the sides of the angle, then it lies on the bisector of the angle
Circumcenter Theorem
The circumcenter of a triangle is equidistant from the vertices of the triangle
Incenter Theorem
The incenter of a triangle is equidistant from the sides of the triangle.
Centroid Theorem
The centroid of a triangle is located 2/3 of the distance from each vertex to the midpoint of the opposite side.
Triangle Midsegment Theorem
A midsegment of a triangle is parallel to the side of a triangle, and its length is half the length of that side.
Triangle Inequality
The sum of any 2 sides is > the third side (used to determine if 3 lengths can form a triangle OR to find the possible lengths of a 3rd side)
Hinge Theorem
If two sides of one triangle are congruent to two sides of another triangle and the included angles are not
Converse of the Hinge Theorem
If two sides of one triangle are congruent to two sides of another triangle, and the third sides are not congruent,
Converse of the Pythagorean Theorem
If a^2 + b^2 = c^2, then the triangle is a right triangle, where a and b are the lengths of the legs and c is the length of the hypotenuse of the triangle.