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?

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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)