Chapter 4: Theorems And Postulates Flashcards
Corollary of Triangle Sum Theorem (right triangles)
The acute angles if a right triangle ate complementary
Triangle sum theorem
The sum of the angle measures of a triangle is 180 degrees
Corollary of the Triangle sum theorem (equilateral triangles)
The measure if each angle if an equiangular triangle is 60 degrees
Exterior angle theorem
The measure of an exterior angle of a triangle is equal to the sum of the measures of its remote interior angles
If two angles of one triangle are congruent to two angles of another triangle, then the third pair of angles are congruent
Third angles theorem
If three sides of one triangle are congruent to three sides if another triangle, then the triangles are congruent
SSS (Side side side congruence 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.
SAS (Side Angle Side Congruence 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
ASA (angle side angle triangle congruence postulate)
If two angles and the included side of one triangle Rare congruent to the corresponding angles Nc the nonincluded side of another triangle, then the triangles are congruent.
AAS (angle angle side triangle congruence postulate)
If the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and a leg of another right triangle, then the triangles are congruent
HL (hypotenuse leg triangle congruence postulate)
If two sides of a triangle are congruent, then the angles opposite the sides are congruent
Isosceles Triangle Theorem
If two angles of a triangle are congruent, then the sides opposite the sides are congruent
Converse of the isosceles triangle theorem
Corollary of the isosceles triangle theorem (equilateral)
If a triangle is equilateral, then it is equiangular
Corollary of the isosceles triangle theorem (equiangular)
Equiangular triangles are equilateral
If a point is on the perpendicular bisector of a segment, then it is equidistant From the endpoints of the segment
Perpendicular bisector segment
If a point is equidistant from the endpoints of a segment, then it is on the perpendicular bisector of the segment
Converse of the perpendicular bisector theorem
If a point is on the bisector on an angle, then it is equidistant from the sides of the angle
Angle bisector theorem
If a point in the interior of an angle is equidistant from the sides of the angle, then it is on the bisector of the angle
Converse of the angle bisector theorem
The circumcenter of a triangle is equidistant from the vertices of the triangle
Circumcenter theorem
The Incenter of a triangle is equidistant from the sides of the triangle
Incenter theorem
The centroid of a triangle is located 2/3 of the distance from each vertex to the midpoint if the opposite side
Centroid theorem
A midsegment of a triangle is parallel to a side of a triangle, and it’s length is half the length of that side
Triangle midsegment theorem
If two sides of a triangle are not congruent, then the larger angle is opposite the longer side
Thm: in triangle larger angle opposite larger side
If two angles of a triangle are not congruent, then the longer side is opposite the larger angle
Thm: in triangle larger side is opposite larger angle
The sum of any two side-lengths of a triangle is greater than the third side-length
Triangle inequality theorem
If two sides of one triangle are congruent to two sides of another triangle and the included angles are not congruent, then the longer third side is across from the larger included angle
Hinge theorem
If two sides of one triangle are congruent to two sides of another triangle and the third sides are it congruent, then the larger included angle is across from the longer third side
Converse of the hinge theorem
