• A man and his wife have three
sons, and every one of the sons
has a sister…
• How many people are there in the
family?
• A. 6
B. 8
C. 10
D. 12
Warm up
1. Identify the transformation ∆RST → ∆XYZ.
Reflection over the y  axis
2. Is XY congruent to RS?
Yes
3. What is the length of XY?
Types of
Quadrilaterals
(4-sided figures)
A four sided figure with both
pairs of opposite sides parallel
Skills Check
Do you know these?
D
 x 2  x1 
a2  b2  c2
y 2  y1
m
x 2  x1
2
  y 2  y1 
2
Some Special Properties of
Parallelograms
• Opposite sides are congruent in
length
• Diagonals bisect each other
• Both pairs of opposite sides are
parallel
To Prove
Parallel (use slope
formula)
• Means opposite
sides have the
SAME SLOPE
Sides Congruent
(use distance
formula)
• Means their
distances are the
same
Solve for x.
Solve for x.
A parallelogram with 4 right
angles
Some Special Properties of
Rectangles
• All the properties of a
parallelogram
• Diagonals are congruent
• 4 right angles
To Prove
Parallel (use slope
formula)
• Means opposite
sides have the
SAME SLOPE
4 Right Angles (use
slope formula)
• Means consecutive
sides have opposite
reciprocal slopes
Opposite Sides
Congruent (use
distance formula)
• Means opposite
sides have the
same distance
A parallelogram with 4
congruent sides
Some Special Properties of
Rhombus
• All the properties of a
parallelogram
• Diagonals are perpendicular
• 4 congruent sides
To Prove
Parallel (use slope
formula)
• Means opposite
sides have the
SAME SLOPE
Perpendicular (use
slope formula)
• Means diagonals
have opposite
reciprocal slopes
Sides Congruent
(use distance
formula)
• Means their
distances are the
same
Solve for x in this rhombus.
Rhombus.
1. VY =
2. mZVY
Z
A parallelogram with 4
congruent sides & 4
right angles
Some Special Properties of
Square
•All the properties of a
parallelogram, rectangle,
& rhombus
Solve for x in this square.
Square
1. EJ =
2. HF =
3. mEJF
4. mHGF
A quadrilateral with 2
pairs of consecutive
congruent sides, but
opposites sides are
NOT parallel
Some Special Properties of
Kite
•Diagonals are perpendicular
To Prove
Not Parallel (use slope
formula)
• All sides have a
different slope
2 Pairs of
Consecutive Sides
Congruent (use
distance formula)
• Means two pair
of sides have the
same distance
A quadrilateral with 1
pair of parallel sides
called bases
Have only one pair of opposite sides
that are parallel.
base
leg
leg
base
A quadrilateral with 1
pair of parallel sides
called bases and nonparallel sides are
congruent (legs)
Some Special Properties of
Isosceles Trapezoid
•Diagonals are congruent
To Prove
Bases Parallel (use
slope formula)
• Means 1 pair of
opposite sides have
the SAME SLOPE
Legs Congruent (use
distance formula)
• Means their
distances are the
same
Diagonals Congruent
(use distance
formula)
• Means their
distances are the
same
Classifying Triangles
by Sides
• Equilateral – 3 congruent sides
• Isosceles – 2 congruent sides
• Scalene – No sides congruent
To Prove
Congruent (use distance formula)
• Means their distances are the
same; figure out how many sides
of the triangle have the same
distance
Classwork
Find the Missing Point
Worksheet
Homework
Quadrilaterals and
Parallelograms
Homework Worksheet