Theorems & Postulates – Flashcards
Unlock all answers in this set
Unlock answersquestion
if two angles form a linear pair, then they are supplementary
answer
linear pair theorem
question
if two angles are supplementary to the same angle (or to congruent angles) then they are congruent
answer
congruent supplements theorem
question
all right angles are congruent
answer
right angle congruence theorem
question
if two angles are complementary to the same angle (or to congruent angles) then the two angles are congruent
answer
congruent complements theorem
question
Given collinear points A, B, C and D arranged as shown if line AB is congruent to line CD then line AC is congruent to line BD a__,__b_______c__,__d
answer
common segments theorem
question
vertical angles are congruent
answer
vertical angles theorem
question
if two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent
answer
corresponding angles postulate
question
if two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent
answer
alternate interior angles theorem
question
If two parallel lines are cut by a transversal, then the pairs of alternate exterior angles are congruent
answer
alternate exterior angles theorem
question
if a transversal intersects 2 parallel lines, then the same side interior angles are supplementary
answer
same side interior angles theorem
question
if two coplanar lines are cut by a transversal so that a pair of corresponding angles are congruent, then the two lines are parallel
answer
converse of the corresponding angles postulate
question
Through a point not on a line, there is one and only one line parallel to the given line.
answer
parallel postulate
question
if two coplanar lines are cut by a transversal so that a pair of alternate interior angles are congruent, then the two lines are parallel
answer
converse of the alternate interior angles theorem
question
If two coplanar lines are cut by a transversal so that a pair of alternate exterior angles are congruent, then the two lines are parallel.
answer
converse of the alternate exterior angles theorem
question
If two coplanar lines are cut by a transversal so that a pair of same-side interior angles are supplementary, then the two lines are parallel.
answer
converse of the same side interior angles theorem
question
in a plane, if a line is perpendicular to one of two parallel lines, then it is perpendicular to the other
answer
perpendicular transversal theorem
question
in a coordinate plane, two non-vertical lines are parallel if and only if they have the same slope. any two vertical lines are parallel
answer
parallel lines theorem
question
In a coordinate plane, two nonvertical lines are perpendicular if and only if the product of their slopes is -1. Vertical and horizontal lines are perpendicular.
answer
perpendicular lines theorem
question
A linear pair is two adjacent angles whose exterior sides form a straight line.
answer
definition of a linear pair
question
a theorem whose proof follows directly from another theorem.
answer
corollary
question
the measure of an exterior angle of a triangle is equal to the sum of the measures of its remote interior angles
answer
exterior angle theorem
question
if two angles of one triangle are congruent to two angles of another triangle, then the third pair of angles are also congruent
answer
third angles theorem
question
two angles that are formed by two lines and a transversal and occupy corresponding positions
answer
definition of corresponding angles
question
If three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent.
answer
side-side-side congruence postulate
question
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.
answer
side-angle-side congruence postulate
question
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.
answer
angle-side-angle congruence postulate
question
If two angles and a nonincluded side of one triangle are congruent to the corresponding angles and nonincluded side of another triangle, then the triangles are congruent.
answer
angle-angle-side congruence theorem
question
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.
answer
hypotenuse-leg congruence theorem
question
the angle formed by the legs.
answer
vertex angle
question
If two sides of a triangle are congruent,then the angles opposite the sides are congruent.
answer
isosceles triangle theorem
question
if two angles of a triangle are congruent, then the sides opposite those angles are congruent
answer
converse of isosceles triangle theorem
question
if a triangle is equilateral, then it is equiangular
answer
equilateral triangle corollary
question
if a triangle is equiangular, then it is equilateral
answer
equiangular triangle corollary
question
the points on a line can be put into a one-to-one correspondence with the real numbers
answer
ruler postulate
question
A part of a line with two endpoints.
answer
definition of a line segment
question
if point B lies in the interior of <aoc then m<aob+m<boc=m<AOC
answer
angle addition postulate
