Geometry - 5-6 Theorems

If two lines are parallel, then all points on one line are equidistant from the other line

If three parallel lines cut off equal segments on one transveral, then they cut off equal segments on every transversal.

If a line contains the midpoint of one side of a triangle and is parallel to another side, then it passes through the midpoint of the third side

A segment that joins the midpoints of two sides of a triangle (midsegment) is parallel to the third side and is half as long as the third side

The diagonals of a rectangle are congruent

Angle Measure Intersection

The diagonals of a rhombus are perpendicular

Angle

Each diagonal of a rhombus bisects the opposite angles

The midpoint of the hypotenuse of a right triangle is equidistant to the 3 vertices

If an angle of a parallelogram is a right angle, then the parallelogram is a rectangle

If two consecutive sides of a parallelogram are congruent, then the parallelogram is a rhombus.

Trapezoid

a quadrilateral with exactly one pair of opposite sides parallel

Bases

the parallel opposite sides of a trapezoid

Base angles

two angles that contain a side of the same base of a trapezoid

Median of a trapezoid

a segment that joins the midpoints of the legs of the trapezoid

ABCD is an isosceles trapezoid

Base angles of an isosceles trapezoid are congruent.

The median (aka midsegment) of a trapezoid is: parallel to the bases and has a length = to the average of the bases

If one side longer than second side

Then the angle opposite the first side is larger than the angle opposite the second side

If one angle is larger than the second angle

Then the side opposite the first angle is larger than the side opposite the second angle.

Shortest segment from a point to a line

The perpendicular segment

Sum of lengths of 2 sides of triangle

Longer than the third

Inverse of "if A, then B”

if not A, then not B

Contrapositive of “if A, then B”

if not B, then not A