6.3: Showing Quadrilaterals are Paralellograms Ashton Carlson

A parallelogram is a quadrilateral in which both pairs of opposite sides are parallel

Vocabulary to Know:

Quadrilateral: a four sided figure

Quadrilateral

Parallelogram: A quadrilateral in which both pairs of opposite sides are parallel

Parallelogram

Consecutive Angles: two interior angles lying on the same side of the transversal cutting across two parallel lines

Parallelogram

Supplementary Angles: two angles that equal 180 degrees when added

Supplementary angles
Showing that quadrilaterals are parallelograms is impossible without these four theorems:

Theorem 6.6

If AD is congruent to BC and DC is congruent to AB, then ABCD is a parallelogram

If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram

Theorem 6.7

If angle A s congruent to angle C and angle B is congruent to angle D, then ABCD is a parallelogram

If both opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram

Theorem 6.8

If angle A + angle D= 180 degrees and angle B + angle C equals 180 degrees, then ABCD is a parallelogram

If an angle of a quadrilateral is supplementary to both of its consecutive angles, then the quadrilateral is a parallelogram

Theorem 6.9

Let the midpoint of the diagonals of ABCD be known as E. If DE = EB and AE = EC, then ABCD is a parallelogram

If the diagonals of a quadrilateral bisect eachother, then the quadrilateral is a parallelogram

Appreciate

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