Download Chapter 6 - Sections 4 and 5 - MercyCatholic

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

Find the value of each variable.
v
y
x
w
z
108
v=108,w=36,x=36,y=36,z=36
RHOMBUS PRACTICE

Find the value of each variable.
z
35
v
y
x
w
v=90,w=55,x=55,z=65,y=35
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
B
A
C
D
x=1
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.
x 44
z
y
v
w
37
v=53,w=53,x=44,y=90,z=46
KITE PRACTICE

Find the value of each variable.
80
y
x
52
x=114,y=114
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 PRACTICE
Find the value of each variable.
y
57
z
x
x=57,y=123,z=123
QUADRILATERAL PRACTICE WITH SOLVING
EQUATIONS

Find x. The figure below is a kite.
2x-4
2x
x+6
x=28
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.
A
B
1. ABllCD, ADllBC
Parallelogram
E
2. AB=AD=DC=BC, <A=90
Square
D
C
3. BD is perpendicular to
AC, AB=BC, AD=CD, AB≠AD
Kite
GIVEN THE FACTS, IDENTIFY THE SHAPE.
The figure below is not draw to scale.
A
1. CDllAB, CD≠AB
B
Trapezoid
E
2. AC=BD, BD is not
perpendicular to AC, AB=CD,
AD=BC
D
C
Rectangle
3. <ABC=<BCD=<CDA=<DAB,
AC is perpendicular to BD
Kite
GIVEN THE FACTS, IDENTIFY THE SHAPE.
The figure below is not draw to scale.
A
B
1. Parallelogram ABCD,
AC=BD, AD=DC
E
Square
2. ∆ABC=∆CDA
D
C
Parallelogram
3. ∆BCA=∆DCA, AD≠DC
Kite