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Geometry Honors > Properties of Quadrilaterals > Flashcards

Properties of Quadrilaterals Flashcards

1
Q

Properties of a parallelogram

A
  • Opposites are parallel by definition
  • Opposite sides are congruent
  • Opposite angles are congruent
  • Diagonals bisect each other
  • Any pair of consecutive angles are supplementary
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2
Q

Properties of rectangles

A

[All the properties of a parallelogram apply by definition]

Opposites are parallel by definition

  • Opposite sides are congruent
  • Opposite angles are congruent
  • Diagonals bisect each other
  • Any pair of consecutive angles are supplementary

All angles are right angles
Diagonals are congruent

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3
Q

Properties of kites

A
  1. Two disjoint paris of consecutive sides are congruent by definition
  2. The diagonals are perpendicular
    3.One diagonal is the perpendicular bisector of the other
    4.One of the diagonals bisects a pair of opposite angles
    5.One pair of opposite angles are congruent
    Rules 3-5 are sometimes called the half properties of kites
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4
Q

Properties of rhombuses

A

[All properties of a parallelogram apply by definition]
Opposites are parallel by definition
-Opposite sides are congruent
-Opposite angles are congruent
-Diagonals bisect each other
-Any pair of consecutive angles are supplementary

[All the properties of a kite apply (the half properties of a kite become full properties)]

Diagonal is the perpendicular bisector of the other
4. of the diagonals bisects angles
5. opposite angles are congruent
All sides are congruent- that is, a rhombus is equilateral
-The diagonals bisect the angles
-The diagonals are the perpendicular bisectors of each other
-The diagonals divide the rhombus into four congruent right triangles

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5
Q

Properties of squares

A

[All the properties of a rectangle apply by definition]
All angles are right angles
Diagonals are congruent

All the properties of a parallelogram apply by definition
Opposites are parallel by definition
-Opposite sides are congruent
-Opposite angles are congruent
-Diagonals bisect each other
-Any pair of consecutive angles are supplementary

[All the properties of a rhombus apply by definition]
Diagonal is the perpendicular bisector of the other
4. of the diagonals bisects angles
5. opposite angles are congruent
All sides are congruent- that is, a rhombus is equilateral
-The diagonals bisect the angles
-The diagonals are the perpendicular bisectors of each other
-The diagonals divide the rhombus into four congruent right triangles

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6
Q

Properties of Isosceles trapezoids

A
  • Legs are congruent by definition
  • The bases are parallel by definition of a trapezoid
  • The lower base angles are congruent
  • The upper base angles are congruent
  • The diagonals are congruent
  • Any lower base angle is supplementary to any upper base angle
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7
Q

If the figure is an isosceles trapezoid, the following are T/F:

  1. The opposite sides are congruent
  2. Opposite sides are parallel
  3. The diagonals bisect the angles
  4. The diagonals bisect each other
  5. The diagonals are congruent
A
  1. T
  2. F
  3. F
  4. F
  5. T
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8
Q

With a kite, the following are T/F:

  1. The opposite sides are congruent
  2. Opposite sides are parallel
  3. The diagonals bisect the angles
  4. The diagonals bisect each other
  5. The diagonals are congruent
  6. The diagonals are perpendicular
A
  1. F
  2. F
  3. T/F
  4. T/F
  5. F
  6. T
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9
Q

What is an equilateral that is not equiangular

A

Rhombus

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10
Q

What is an equiangular quadrilateral that is not equiangular

A

Rectangular

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11
Q

Always true, sometimes true, or never true

  1. A square is a rhombus
  2. A rhombus is a square
  3. A kite is a parallelogram
  4. A rectangle is a polygon
  5. A polygon has the same number of vertices as sides
  6. A parallelogram has three diagonals
  7. A trapezoid has three bases
A
  1. Always
  2. Sometimes
  3. Sometimes- when a kite is a rhombus
  4. Always- A rectangle=parallelogram=quadrilateral
  5. Always- parallelograms only have 2
  6. Never
  7. Never
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12
Q

The following methods can be used to prove that a rhombus-like rectangle is a parallelogram. PROVING THAT A QUADRILATERAL IS A PARALLELOGRAM

A
  1. If both pairs of opposite sides of a quadrilateral are parallel, then the quadrilateral is a parallelogram (reverse of definition)
  2. If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram (converse of property)
  3. If one pair of opposite sides of a quadrilateral are both parallel and congruent, then the quadrilateral is a parallelogram
  4. If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram (converse of a property)
  5. If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram (converse of a property)
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13
Q

Prove that a quadrilateral is a rectangle

A
  1. Show that a quadrilateral is a parallelogram
  2. If a parallelogram contains at least one right angle, then it is a rectangle (reverse of definition)

You can also prove that a quadrilateral is a rectangle without first showing that it is a parallelogram
3. If all four angles of a quadrilateral are right angles, then it is a rectangle

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14
Q

Prove that a quadrilateral is a kite

A
  1. If two disjoint pairs of consecutive sides of a quadrilateral are congruent then it is a kite (reverse of the definition)
  2. If one of the diagonals of a quadrilateral is the perpendicular bisector of the other diagonal, then the quadrilateral is a kite
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15
Q

Proving that a quadrilateral is a rhombus

A
  1. Show that is is a parallelogram
  2. If if a parallelogram contains a pair of consecutive sides that are congruent, then it is a rhombus (reverse of definition)
  3. If either diagonal of a parallelogram bisects two angles of the parallelogram, then it is a rhombus

You can prove that a quadrilateral is a rhombus without first showing that it is a parallelogram
4. If the diagonals of a quadrilateral are perpendicular bisectors of each other, then the quadrilateral is a rhombus

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16
Q

Proving that a quadrilateral is a square

A

If a quadrilateral is both a rectangle and a rhombus, then it is a square

17
Q

Proving that a trapezoid is isosceles

A
  1. Is the nonparallel sides of a trapezoid are congruent, then it is isosceles (reverse of definition)
  2. If the lower or the upper base angles of a trapezoid are congruent, then it is isosceles
  3. If the diagonals of a trapezoid are congruent, then it is isosceles

Geometry Honors (2 decks)

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