Chapter 5 - Quadrilaterals

A quadrilateral with both sides parallel DEFINITION OF PARALLELOGRAM

if a QUADRILATERAL IS A PARALLELOGRAM, then OPPOSITE SIDES are CONGRUENT

if a QUADRILATERAL IS A PARALLELOGRAM, then OPPOSITE ANGLES are CONGRUENT

If a QUADRILATERAL IS A PARALLELOGRAM, then its DIAGNOLS BISECT EACHOTHER

NOW GOING INTO WAYS TO PROVE SOMETHING IS A PARALLELOGRAM

If BOTH PAIRS OF OPPOSITE SIDES of a quadrilateral ARE CONGRUENT then the QUADRILATERAL IS A PARALLELOGRAM, definition of parralelogram

If BOTH PAIRS OF OPPOSITE ANGLES of a quadrilateral ARE CONGRUENT then the QUADRILATERAL IS A PARALLELOGRAM,

If THE DIAGNOLS OF A QUADRILATERAL BISECT each other then the QUADRILATERAL IS A PARALLELOGRAM

If ONE PAIR OF OPPOSITE SIDES of a quadrilateral are both CONGRUENT AND PARALLEL then the QUADRILATERAL IS A PARALLELOGRAM

NOW GOING INTO THEORUMS INVOLVING PARALLEL LINES

If TWO LINES ARE PARRALEL then all POINTS ON ONE LINE are EQUIDISTANT FROM THE OTHER LINE

If THREE PARALLEL LINES CUT off CONGRUENT SEGMENTS on ONE TRANSVERSAL then they CUT OFF CONGRUENT SEGMENTS on EVERY TRANSVERSAL

A line that CONTAINS the MIDPOINT of ONE SIDE OF A TRIANGLE and is PARALLEL TO ANOTHER SIDE PASSES THROUGH THE MIDPOINT OF THE THIRD SIDE

The SEGMENT that JOINS THE MIDPOINTS of two sides of a triangle is…(1) PARALLEL to the THIRD SIDE;(2)HALF as long as the THIRD SIDE (Remember 27’s, 2 parts to this)

NOW GOING INTO SPECIAL PARALLELOGRAMS

Rectangle: A quadrilateral with 4 right angles

Rhombus: A quadrilateral with 4 congruent sides

Square: A quadrilateral with 4 congruent sides and 4 right angles

The diagnols of a rectangle are congruent

2 theorums for this

1: The diagonals of a rhombus are perpendicular (AC is perpendicular to DB)
2: Each diagonal of a rhombus bisects two angles of the rhombus

Diagonals of a parallelogram bisect each other, Diagonals of a rectangle are congruent, so what do we know about point A?

The MIDPOINT of the HYPOTENUSE of a RIGHT TRIANGLE is EQUIDISTANT FROM THE THREE VERTICES(median)

If an ANGLE of a PARALLELOGRAM is a RIGHT ANGLE then the parralelogram is a RECTANGLE

If TWO CONSECUTIVE SIDES of a PARALLELOGRAM ARE CONGRUENT then the parrallelogram is a RHOMBUS

Yes because diagnols are congruent

Rectangle, parralelogram diagnols are congruent

NOW GOING INTO TRAPEZOIDS

Trapezoid: A quadrilateral with only one pair of parallel sides

Isoceles Trapezoid: A trapezoid with congruent legs

Base angles of an isoceles trapezoid are congruent

Median of a trapezoid: Segment that joins the midpoints of the legs

The median of a trapezoid is 1: _
The median of a trapezoid is 2: _

1: parallel to the bases
2: Has a length equal to the avg of the bases