Geometry Notes
Lesson 4.1B
Special Quadrilaterals
Parallelogram
Parallelogram – a quadrilateral with two pairs of opposite sides parallel
Properties of parallelograms
Opposite sides are congruentOpposite angles are congruentDiagonals 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 perpendicularEach 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
Diagonals are perpendicular One diagonal is bisected
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. False!
Some kites are rectangles. False!
Some parallelograms are rectangles. True!
Some trapezoids are parallelograms. False!
All squares are kites. False!
All squares are rectangles. True!
True or False? All parallelograms are kites. All rectangles are squares. Some kites are squares. All kites are quadrilaterals.
False!
False!
False!
True!
Name ALL special quadrilaterals that satisfy the following conditions.
Both pairs of opposite sides are parallel
Diagonals are perpendicular
All angles are right angles
Parallelogram, rectangle, rhombus, square
rhombus, square, kite
rectangle, square
Name ALL special quadrilaterals that satisfy the following conditions.
Two pairs of opposite sides are equal
All four sides are equal
Both pairs of opposite angles are equal
Parallelogram, rectangle, rhombus, square
rhombus, square
Parallelogram, rectangle, rhombus, square
Name ALL special quadrilaterals that satisfy the following conditions.
Diagonals bisect each other
Both diagonals are equal
Only one pair of sides is parallel
All adjacent pairs of angles are supplementary
Parallelogram, rectangle, rhombus, square
Rectangle, square, Isosceles Trapezoid
Trapezoid, Isosceles Trapezoid
Parallelogram, rectangle, rhombus, square
Fill in the Venn Diagram
Given labels: Parallelograms, Kites, Rectangles
Quadrilaterals
Trapezoids
Squares Rhombuses
EXAMPLES
Draw a quadrilateral with two pairs of opposite parallel sides on the graph.
-5 -1-2-3-4 1 2 3 4
1
2
3
4
5
-1
-2
-3
-4
Examples
Draw a quadrilateral with two pairs of congruent adjacent sides on the graph.
-1-2-3-4 1 2 3 4
1
2
3
4
5
-1
-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)
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