Definition of congruence
Reflexive property of Congruence
AB is congruent to AB
Definition of a straight line
An undefined term in geometry, a line is a straight path that has no thickness and extends forever. It also forms a straight angle which measures 180°
Alternate exterior angle
Angles that lie outside a pair of lines and on opposite sides of a transversal.
Reflexive property of Equality
Any measure equal to itself
Definition of Supplementary Angles
Any two angles that have a sum of 180°
Linear Pair Theorem
If 2 angles form a linear pair, then they are supplementary
Side-side-side postulate
If 3 sides of one triangle are congruent to 3 sides of another triangle, then the triangles are congruent
Segment Addition Postulate
If B is between A and C, then AB + BC = AC
Angle Addition Postulate
If P is in the interior of <RST, then m<RSP + m<PST = m<RST
Triangle mid segment theorem
If a segment joins the midpoints of two sides of a triangle, then the segment is parallel to the third side and is half as long.
Same-side interior angles theorem
If a transversal intersects two parallel lines, then same-side interior angles are supplementary.
Transitive property
If a=b and b=c, then a=c
Addition property of Equality
If a=b, then a+c=b+c
Division Property of Equality
If a=b, then a-c=b-c
Subtraction property of equality
If a=b, then a-c=b-c
Multiplication Property of Equality
If a=b, then ac=bc
Hypotenuse -leg postulate
If the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and corresponding leg of another right triangle, then the triangles are congruent
Pythagorean Theorem Converse
If the square of one side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is a right triangle.
Right angle theorem
If two angles are right angles, then they are congruent.
Third Angles Theorem
If two angles of one triangle are congruent to two angles of another triangle, then the third angles are also congruent.
Alternate interior angle theorem
If two parallel lines are cut by a transversal, then the alternate interior angles are congruent.
Corresponding angle theorem
If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent
Side-angle-side 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 two triangles are congruent.
Isosceles Triangle Theorem
If two sides of a triangle are congruent, then the angles opposite those sides are congruent.
Definition of Perpendicular Lines
Lines that intersect to form right angles or 90°
Definition of midpoint
The point that divides a segment into two congruent segments.
Definition of Angle Bisector
The ray that divides an angle into two congruent angles.
Triangle sum theorem
The sum of the measures of the interior angles of a triangle is 180 degrees
Vertical Angle Theorem (VAT)
Vertical angles are congruent
CPCTC
corresponding parts of congruent triangles are congruent
Angle angle Side postulate
two angles and the unincluded side of a triangle are congruent to two angles and the unincluded side of another triangle