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Parallelogram.
• DEFINITION:
Parallelograms are quadrilaterals with
both pairs of opposite sides parallel.
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D
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Quadrilateral.
DEFINITION:
Quadrilateral just means "four sides"
(quad means four, lateral means side).
Any four-sided shape is a Quadrilateral.
But the sides have to be straight, and it has to be 2dimensional.
RECTANGLES
PARALLELOGRAMS
QUADRILATERALS
RHOMBI
SQUARES
5 Things About
Parallelograms
DEFINITION
1) Both Pairs Opp Sides Parallel
PROPERTIES
2) Both Pairs Opp Sides Congruent
3) Both Pairs Opp Angles Congruent
4) Consecutive Angles Supplementary
5) Diagonals Bisect Each Other
SPECIAL CASES:
• RHOMBOID – A quadrilateral whose opposite sides
are parallel and adjacent sides are unequal, and whose
angles are not right angles
• RECTANGLE – A parallelogram with four angles of
equal size
• RHOMBUS – A parallelogram with four sides of equal
length.
• SQUARE – A parallelogram with four sides of equal
length and angles of equal size (right angles).
Proof of Theorem:
If a quadrilateral is a parallelogram, the 2 pairs of opposite
sides are congruent.
STATEMENTS
REASONS
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2 Draw segment from A to C
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Given
Two points determine exactly one line.
A parallelogram is a quadrilateral with both
pairs of opposite sides parallel.
If two parallel lines are cut by a transversal,
the alternate interior angles are congruent.
Reflexive property: A quantity is congruent
to itself.
ASA: If two angles and the included side of
one triangle are congruent to the
corresponding parts of another triangle, the
triangles are congruent.
CPCTC: Corresponding parts of congruent
triangles are congruent.