theorems page 2 Flashcards
reflections in intersecting Lines theorem
if lines K and M intersect at point P, then a reflection in-line K followed by a reflection in line M is the same as a rotation about. P. The angle of rotation is 2X , where X is the measure of the acute or right angle formed by lines K and M
triangle sum theorem
The sum of the measures of the interior angles of a triangle is 180
exterior angle theorem
The measure of an exterior angle of a triangle is equal to the sum of the measures of the two nonadjacent interior angles
corollary to the triangle sum theorem
The acute angles of a right triangle are complementary
third angles theorem
if two angles of one triangle are congruent to two angles of another triangle then the third angles are also congruent
Side – angle – side congruence theorem
if two sides and the included angle of one triangle are congruent to two sides and the included angle of a second triangle then the two triangles are congruent
bass angles theorem
if two sides of a triangle are congruent then the angles opposite of them are congruent
Converse of the base angles theorem
if two angles of a triangle are congruent then the sides opposite them are congruent
corollary to the base angles theorem
if a triangle is equal lateral then it is equiangular
corollary to the converse of the base angles theorem
if a triangle is equiangular then it is equal lateral
Side – side – side congruence theorem
if three sides of one triangle are congruent to three sides of the second triangle then the two triangles are congruent
hypotenuse – leg congruence theorem
if the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and leg of a second right triangle then the two triangles are congruent
angle – Side – angle congruence theorem
if two angles and the included side of one triangle are congruent to two angles and the included side of a second triangle then the two triangles are congruent
angle – angle – side congruence theorem
if two angles and did not included Side of one triangle are congruent to two angles any corresponding non-included side of the second triangle then the two triangles are congruent
perpendicular bisector theorem
any point if a point lies on the perpendicular bisector of a segment then it is equidistant from the endpoints of the segment
Converse of the perpendicular bisector theorem
in a plane, if a point is equidistant from the endpoints of a segment then it lies on the perpendicular bisector of the segment
angle bisector theorem
if a point lies on the bisector of an angle that it is equidistant from the two sides of an angle
Converse of the angle by sector theorem
if a point is in the interior I’ve been angle and is equidistant from the two sides of the angle that it lies on the bisector of the angle
circumcenter theorem
The circumcenter of a triangle is equidistant from the vertices of the triangle
in center theorem
The in center of a triangle is equidistant from the sides of the triangle
centroid theorem
The centroid of a triangle is two thirds the distance from each vertex to the midpoint of the opposite side