Geometry- Lesson 22

POSTULATES

-A statement accepted as true without a proof. -Specific to geometry. -Unproved, but agreed upon.

THEOREMS

-A statement that must be proved before accepted as true. -Axioms and postulates are used in this process.

Alternate Exterior Angles

-Angles that lie outside a pair of lines and on opposite sides of a transversal. -Alternate Exterior Angles are congruent

Alternate Interior Angles Theorem

-Interior angles that lie on opposite sides of the transversal -Alternate interior angles are congruent

AXIOM

-Universal agreed upon truths. -Obvious statements that make sense. -Assumptions

SUM OF EXTERIOR ANGLES

360 degrees

RHOMBUS

A parallelogram with four congruent sides

SQUARE

A parallelogram with four congruent sides and four right angles.

TRAPEZOID

A quadrilateral with exactly one pair of parallel sides

PARALLELOGRAM

A quadrilateral with two pairs of parallel sides

Angle Bisector

A ray that divides an angle into 2 congruent angles

ISOSCELES TRIANGLE

A triangle with at least two congruent sides

PARALLEL LINES

Coplanar lines that do not intersect

Midpoint Theorem

If M is the midpoint of AB, then AM is congruent to MB

SYMMETRY PROPERTY

If a = b, then b = a

TRANSITIVE PROPERTY

If a=b and b=c, then a=c

PYTHAGOREAN THEOREM

LEG^2 + LEG^2 = HYPOTENUSE^2

TRIANGLE INEQUALITY THEOREM

The sum of the lengths of any two sides of a triangle is greater than the length of the third side.

Triangle Angle Sum Theorem

The sum of the measures of the angles of a triangle is 180.

SUPPLEMENTARY ANGLES

Two angles whose sum is 180 degrees

COMPLEMENTARY ANGLES

Two angles whose sum is 90 degrees

PERPENDICULAR LINES

Two lines that intersect to form right angles

Vertical Angles Theorem

Vertical angles are congruent

REFLEXIVE PROPERTY

a = a

RECTANGLE

a parallelogram with 4 right angles

REGULAR POLYGON

a polygon that is both equilateral and equiangular

CONGRUENT ANGLES

angles that have the same measure or equal measure

CORRESPONDING ANGLES

the angles that occupy the same relative position at each intersection where a straight line crosses two others. If the two lines are parallel, the corresponding angles are equal.

CONGRUENT LINE SEGMENTS

two line segments with equal lengths