5-4 notes - Barrington High School

5­4 notes
Directions:
Special Quads.gsp
1. Find a partner with the same group number as you.
2. Follow the instructions and record your results for each of the 6 remaining quadrilaterals.
3. When done, leave your partner and find a partner with a different group.
4. Explain your instructions to your new partner and share your recorded findings with them.
5. When both of you have recorded each other's findings in your tables, split up and find a new group.
6. Repeat this process until your entire table is complete.
Group 1
Group 2
Group 3
Group 4
Group 5
5­4 chart.xlsx
Extra Practice
x=10
1.
A
D
HW page 187-189 #1-19
2.
x = 2
B
C
x = 1
1
2
1

5­4 notes
Practice: Rhombus
Find the measures of the numbered angles
in the rhombus.
2
72°
11 72
90
90
3
1 4 90
5
90
18
6 18
72 72
7 8
1810
9
18
Example #1: Rhombus
Find the measures of the numbered angles in the rhombus.
50°
40 2
90
1
Example #2: Rhombus ABCD
• If m

5­4 notes
Example #4: Rectangle ABCD
Example #5: Rectangle ABCD
BF = 5, find AC and BD.
both = 10
A
D
A
D
F
E
B
C
B
C
Example #7: Square ABCD
Find all measurements.
A
B
2 More Theorems from this section...
If an angle of a parallelogram is a right angle,
then the parallelogram is a ________.
5
E
If two consecutive sides of a parallelogram are
congruent, then the parallelogram is a ________.
C
D
3

5­4 notes
Recap:
The diagonals of a rectangle are _______.
The diagonals of a rhombus are _______.
Each diagonal of a rhombus_______ two angles
of the rhombus.
The midpoint of the hypotenuse of a right triangle
is equidistant from the _____ vertices.
Parallelogram: A quadrilateral with both pairs of opposite sides parallel.
Both pairs of opposite sides are also congruent. The symbol for a
parallelogram is .
Rhombus: a parallelogram with four congruent sides.
Rectangle: a parallelogram with four right angles.
Square: a parallelogram with four congruent sides and four right angles.
Kite: a quadrilateral with two pairs of adjacent sides congruent and no
opposite sides congruent.
Trapezoid: a quadrilateral with exactly one pair of parallel sides.
Isosceles trapezoid: a trapezoid whose nonparallel sides are congruent.
5.4 Special Parallelograms
Parallelogram: A quadrilateral with both pairs of
opposite sides parallel. Both pairs of opposite sides
are also congruent.
The symbol for a parallelogram is .
Q: Not all parallelograms look the same. What is the
name of one special type of parallelogram? Name some
other special types.
A:
Rectangle: A parallelogram with four right angles.
Rhombus: A parallelogram with four sides.
Square: A rectangle with four sides or
a rhombus with four right angles.
4

5­4 notes
Do Now: An SAT problem…
In the figure below, MNOP is a parallelogram. What is
the value of x?
x=10
M
N
15x° (40­x)°
Properties of a Rectangle
• Four right angles.
• Diagonals are congruent.
Example of a rectangle:
P
O
Properties of a rhombus
• Diagonals of a rhombus are perpendicular.
• All sides of a rhombus are congruent.
• Diagonals bisect the angles of a rhombus.
Example:
Properties of a Square
• Diagonals of a square are perpendicular.
• All sides of a square are congruent.
• Diagonals bisect the angles of a square.
• Four right angles.
• Diagonals are congruent.
Example of a Square:
5

Attachments
Special Quads.gsp
5­4 chart.xlsx