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