Properties of special quadrilaterals

PROPERTIES OF SPECIAL QUADRILATERALS

PROPERTIES OF RHOMBUSES 1. 4 congruent sides (definition) 2. All properties of Parallelograms 3. The diagonals of a rhombus are

perpendicular. 4. Each diagonal bisects a set of

opposite angles.

RHOMBUS PRACTICE

108

x

z

y

w

Find the value of each variable.

v=108,w=36,x=36,y=36,z=36

v

RHOMBUS PRACTICE

35

x

z

y w

Find the value of each variable.

v=90,w=55,x=55,z=65,y=35

v

PROPERTIES OF A RECTANGLE 1. 4 Right Angles (definition) 2. All Properties of Parallelograms 3. Diagonals are congruent (the same

length)

RECTANGLE PRACTICE Find x, given that AC=3x+1 and BD=8x-4

x=1

AB

C D

PROPERTIES OF KITES 1. No sets of parallel sides (Definition) 2. Two sets of congruent sides which

are adjacent to each other (Definition) 3. Diagonals are perpendicular. 4. One of the diagonals bisects a set of

opposite angles

KITE PRACTICE Find the value of each variable.

v=53,w=53,x=44,y=90,z=46

vwz y

x 44

37

KITE PRACTICE Find the value of each variable.

x=114,y=114

yx

52

80

PROPERTIES OF TRAPEZOIDS 1. One set of parallel sides (Definition) 2. Two sets of same side interior angles

are supplementary (parallel line required)

PROPERTIES OF ISOSCELES TRAPEZOIDS 1. All properties of Trapezoids 2. Two congruent legs (Definition) 3. Sets of base angles are congruent 4. The diagonals are congruent

TRAPEZOID PRACTICEFind the value of each variable.

x=57,y=123,z=123

zy

x57

QUADRILATERAL PRACTICE WITH SOLVING EQUATIONS

Find x. The figure below is a kite.

x=28

2x-4

2x

x+6

HOMEWORK Regular Geometry: WKST 6.4 and 6.5 Honors Geometry:

GROUP WORK P 316 (25-34)

Fill in the chart based on the properties of each Quadrilateral we have discussed.

GIVEN THE FACTS, IDENTIFY THE SHAPE.

The figure below is not draw to scale.1. ABllCD, ADllBCParallelogram2. AB=AD=DC=BC, <A=90Square3. BD is perpendicular to AC, AB=BC, AD=CD, AB≠ADKite

E

C

BA

D

GIVEN THE FACTS, IDENTIFY THE SHAPE.

The figure below is not draw to scale.1. CDllAB, CD≠ABTrapezoid2. AC=BD, BD is not perpendicular to AC, AB=CD, AD=BCRectangle3. <ABC=<BCD=<CDA=<DAB, AC is perpendicular to BDsquare

E

C

BA

D

GIVEN THE FACTS, IDENTIFY THE SHAPE.

The figure below is not draw to scale.1. Parallelogram ABCD, AC=BD, AD=DCSquare2. ∆ABC=∆CDAParallelogram3. ∆BCA=∆DCA, AD≠DCKite

E

C

BA

D