5.5 Properties of Quadrilaterals

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5.5 Properties of Quadrilaterals

• Objectives
• Know properties of special quadrilaterals.
• Use properties of special quadrilaterals in proofs

5.4
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parallelograms a quadrilateral with both pairs
of opposite sides parallel.
Opposite sides are congruent. Opposite angles are
congruent.
Consecutive angles are supplementary. Diagonals
bisect each other.
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rhombus a quadrilateral with all sides
congruent.
All sides congruent. Diagonals are . Diagonals
bisect angles. Diagonals create 4 congruent
triangles.
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rectangle a quadrilateral with all right angles
All angles are right angles. Diagonals are
congruent.
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square a quadrilateral that is both a rectangle
and a rhombus
Diagonals form 4 congruent isosceles right
triangles.
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kite a quadrilateral in which 2 pairs of
consecutive sides are congruent, but opposite
sides are not congruent
Exactly 1 pair of opposite angles
congruent. Diagonals are Diagonal bisects non-
_at_ angles. Diagonal bisects other diagonal.
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trapezoid a quadrilateral with exactly 1 pair
of parallel sides
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isosceles trapezoid a trapezoid with the
non-parallel sides congruent (legs)
Pairs of base angles are congruent. Diagonals are
congruent. Upper base angles and lower base
angles are supplementary.
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Quadrilaterals (4 sides)
Trapezoid - (1 pr of opp. sides ll)
Kites - (2 prs of cons. _at_ sides)
Parallelograms (opp. sides ll)
Isosceles Trap. (legs are _at_)
Rhombus (all sides _at_)
Rectangles (all right Ðs)
Square (Rect Rhomb)
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Property ll rect rhm sqr kite trp istrp
Both pairs of opposite sides parallel
Exactly 1 pair of opposite sides parallel
Diagonals perpendicular
Diagonals congruent
Diagonals bisect each other
Both pairs of opposite sides are congruent
Exactly one pair of opposite sides are congruent
All sides are congruent
Both pairs of opposite angles are congruent
Exactly one pair of opposite angles are congruent
All angles are congruent
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Property ll rect rhm sqr kite trp istrp
Both pairs of opposite.sides parallel X
Exactly 1 pair of opposite sides parallel
Diagonals perpendicular
Diagonals congruent
Diagonals bisect each other X
Both pairs of opposite sides are congruent X
Exactly one pair of opposite sides are congruent
All sides are congruent
Both pairs of opposite angles are congruent X
Exactly one pair of opposite angles are congruent
All angles are congruent
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Property ll rect rhm sqr kite trp istrp
Both pairs of opposite.sides parallel X X
Exactly 1 pair of opposite sides parallel
Diagonals perpendicular
Diagonals congruent X
Diagonals bisect each other X X
Both pairs of opposite sides are congruent X X
Exactly one pair of opposite sides are congruent
All sides are congruent
Both pairs of opposite angles are congruent X X
Exactly one pair of opposite angles are congruent
All angles are congruent X
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Property ll rect rhm sqr kite trp istrp
Both pairs of opposite.sides parallel X X X
Exactly 1 pair of opposite sides parallel
Diagonals perpendicular X
Diagonals congruent X
Diagonals bisect each other X X X
Both pairs of opposite sides are congruent X X X
Exactly one pair of opposite sides are congruent
All sides are congruent X
Both pairs of opposite angles are congruent X X X
Exactly one pair of opposite angles are congruent
All angles are congruent X
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Property ll rect rhm sqr kite trp istrp
Both pairs of opposite.sides parallel X X X X
Exactly 1 pair of opposite sides parallel
Diagonals perpendicular X X
Diagonals congruent X X
Diagonals bisect each other X X X X
Both pairs of opposite sides are congruent X X X X
Exactly one pair of opposite sides are congruent
All sides are congruent X X
Both pairs of opposite angles are congruent X X X X
Exactly one pair of opposite angles are congruent
All angles are congruent X X
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Property ll rect rhm sqr kite trp istrp
Both pairs of opposite.sides parallel X X X X
Exactly 1 pair of opposite sides parallel
Diagonals perpendicular X X X
Diagonals congruent X X
Diagonals bisect each other X X X X
Both pairs of opposite sides are congruent X X X X
Exactly one pair of opposite sides are congruent
All sides are congruent X X
Both pairs of opposite angles are congruent X X X X
Exactly one pair of opposite angles are congruent X
All angles are congruent X X
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Property ll rect rhm sqr kite trp istrp
Both pairs of opposite.sides parallel X X X X
Exactly 1 pair of opposite sides parallel X
Diagonals perpendicular X X X
Diagonals congruent X X
Diagonals bisect each other X X X X
Both pairs of opposite sides are congruent X X X X
Exactly one pair of opposite sides are congruent
All sides are congruent X X
Both pairs of opposite angles are congruent X X X X
Exactly one pair of opposite angles are congruent X
All angles are congruent X X
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Property ll rect rhm sqr kite trp istrp
Both pairs of opposite.sides parallel X X X X
Exactly 1 pair of opposite sides parallel X X
Diagonals perpendicular X X X
Diagonals congruent X X X
Diagonals bisect each other X X X X
Both pairs of opposite sides are congruent X X X X
Exactly one pair of opposite sides are congruent X
All sides are congruent X X
Both pairs of opposite angles are congruent X X X X
Exactly one pair of opposite angles are congruent X
All angles are congruent X X