Download Definitions, Properties and Theorems as Conditionals

Definitions, Properties and Theorems as Conditionals
If a segment bisects another segment,
Definition of segment bisector
then it intersects at its midpoint.
If a point is a midpoint,
then it divides a segment into 2  segments.
Definition of midpoint
,
If
Definition of congruent segments
.
then
,
If
Definition of congruent angles
.
then
If two lines are perpendicular,
Definition of perpendicular lines
then they form right angles.
If two lines form right angles,
Definition of perpendicular lines
then they are perpendicular.
If an angle is right,
Definition of right angle
then its measure is 90.
If an angle’s measure is 90,
Definition of right angle
then it is a right angle.
If a ray bisects an angle,
Definition of angle bisector
then it forms 2  angles.
If
B
A
C
Segment Addition Postulate
then
If
.
R
A
B
C
Angle Addition Postulate
then
.
If a triangle is isosceles,
then it has at least 2  sides.
If a triangle has at least 2  sides,
then it is isosceles.
Definition of isosceles triangle
Definition of isosceles triangle
If two angles are right angles,
then they are congruent.
If
A
All right angles are congruent.
B
Reflexive Property of Congruence
then
.
If
and
then
If
.
1
Transitive Property of Congruence
2
then 1  2.
If two lines are parallel and cut by a
transversal,
Vertical Angles Theorem
Alternate Interior Angles Theorem
then alternate interior angles are congruent.
If alternate interior angles are congruent,
then the lines are parallel.
Converse of the Alternate Interior
Angles Theorem
If corresponding parts of polygons are ,
then the polygons are congruent
If two triangles are congruent,
then corresponding parts are congruent.
If three sides of one triangle are congruent to
three sides of another triangle,
Definition of congruent polygons
CPCTC
SSS Postulate
then the triangles are congruent.
If 2 sides & the included angle of one triangle are congruent
to 2 sides & the included angle of another triangle,
SAS Postulate
then the triangles are congruent.
If 2 angles & the included side of one triangle are congruent
to 2 angles & the included side of another triangle,
ASA Postulate
then the triangles are congruent.
If 2 angles & the nonincluded side of one triangle are congruent
to 2 angles & the nonincluded side of another triangle ,
AAS Theorem
then the triangles are congruent.
If the hypotenuse and one leg of a right triangle are congruent
to the hypotenuse and leg of a another right triangle,
HL Theorem
then the triangles are congruent.
If two angles of one triangle are congruent to two angles of
another triangle,
then the third angles are .
Third Angle Theorem
If two sides of a triangle are congruent,
then the angles opposite those sides are .
If two angles of a triangle are congruent,
then the sides opposite those angles are .
Isosceles Triangle Theorem
Converse of the Isosceles Triangle
Theorem