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