4.1B Special Quadrilaterals LESSON
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Transcript 4.1B Special Quadrilaterals LESSON
Geometry Notes
Lesson 4.1B
Special Quadrilaterals
Parallelogram
Parallelogram – a quadrilateral with
two pairs of opposite sides parallel
Properties of parallelograms
Opposite sides are congruent
Opposite angles are congruent
Diagonals bisect each other
Rectangle
Rectangle – a parallelogram with
four right angles
Special properties of rectangles
Diagonals are congruent
Rhombus
Rhombus – a parallelogram with
four congruent sides
Special properties of rhombuses
Diagonals are perpendicular
Each diagonal bisects opposite
angles
Square
Square – a parallelogram with
four right angles and four
congruent sides
Special properties of
squares
Diagonals are congruent
Diagonals are perpendicular
Each diagonal bisects opposite
angles
Kite
Kite – A quadrilateral with two
pairs of adjacent sides congruent
and no opposite sides congruent
Special properties of kites
Diagonals bisect 2 of the angles
. One diagonal is bisected
Diagonals are perpendicular
Trapezoid
Trapezoid – A quadrilateral with
exactly one pair of parallel sides
Special properties of trapezoids
Same-Side Interior Angles = 180
Isosceles Trapezoid
Isosceles Trapezoid – a
trapezoid whose nonparallel sides
are congruent
Special properties of isosceles
trapezoids
Nonparallel sides are congruent
. Base Angles are congruent
Diagonals are congruent
The following is a diagram to show
how different quadrilaterals are
related.
True or False?
All parallelograms are squares.
Some kites are rectangles.
False!
False!
Some parallelograms are rectangles.
True!
Some trapezoids are parallelograms.
All squares are kites.
All squares are rectangles.
False!
False!
True!
True or False?
All parallelograms are kites. False!
All rectangles are squares. False!
False!
Some kites are squares.
All kites are quadrilaterals. True!
Name ALL special quadrilaterals that
satisfy the following conditions.
Both pairs of opposite sides are parallel
Parallelogram, rectangle, rhombus, square
Diagonals are perpendicular
rhombus, square, kite
All angles are right angles
rectangle, square
Name ALL special quadrilaterals that
satisfy the following conditions.
Two pairs of opposite sides are equal
Parallelogram, rectangle, rhombus, square
All four sides are equal
rhombus, square
Both pairs of opposite angles are equal
Parallelogram, rectangle, rhombus, square
Name ALL special quadrilaterals that
satisfy the following conditions.
Diagonals bisect each other
Parallelogram, rectangle, rhombus, square
Both diagonals are equal
Rectangle, square, Isosceles Trapezoid
Only one pair of sides is parallel
Trapezoid, Isosceles Trapezoid
All adjacent pairs of angles are
supplementary
Parallelogram, rectangle, rhombus, square
Fill in the Venn Diagram
Given labels: Parallelograms, Kites,
Rectangles
Quadrilaterals
Squares
Rhombuses
Trapezoids
EXAMPLES
Draw a quadrilateral with two pairs of
opposite parallel sides on the graph.
5
4
3
2
1
-5
-4
-3
-2
1
-1
-1
-2
-3
-4
2
3
4
Examples
Draw a quadrilateral with two pairs of
congruent adjacent sides on the graph.
5
4
3
2
1
-4
-3
-2
1
-1
-1
-2
-3
-4
2
3
4
Examples
Use the slope and/or distance formulas to determine the MOST
PRECISE name for the quadrilateral with the given vertices.
A (0, 0); B(5, 5); C(8, 4); D(7, 1)
Examples
Use the slope and/or distance formulas to determine the MOST
PRECISE name for the quadrilateral with the given vertices.
A(2, 1); B(5, -1); C(4, -4); D(1, -2)