Properties of Special Quadrilaterals

1
Properties of Special Quadrilaterals

• Unit 5
• Pg. 304

2
Quadrilateral

• A four sided polygon.
• Property
• The sum of the interior angles is 360º.

3
Parallelogram

• A quadrilateral with both pairs of opposite sides
  parallel.
• Properties
• Both pairs of Opposite Sides are Parallel.
• Both Pairs of Opposite Sides are Congruent.
• Both Pairs of Opposite Angles are Congruent.
• Consecutive angles are Supplementary.
• The Diagonals Bisect each other.
• The Diagonal cuts it into 2 Congruent Triangles.

4
Rectangle

• A parallelogram with 4 Right Angles.
• Properties
• All the properties of a parallelogram.
• Diagonals are Congruent.
• Equiangular.

5
Rhombus

• A parallelogram with 4 Congruent Sides.
• Properties
• All the properties of a parallelogram.
• Diagonals are Perpendicular.
• Diagonals Bisect the pairs of opposite angles.
• Equilateral.

6
Square

• A Rectangle with 4 Congruent Sides
• A Rhombus with 4 Right Angles.
• Properties
• All the properties of a Rectangle.
• All the properties of a Rhombus.

7
Examples

• Sometimes, Always, Never????
• 1. A rectangle is a square.
• 2. A square is a rhombus.
• 3. A rhombus is a rectangle.
• 4. A parallelogram is a rectangle.

8

• 5. QRST is a square. What do you know
• about it?
• a.
• b.
• c.
• d.
• e.
• f.

Q
R
S
T
9

• 6. EFGH is a rectangle. K is the midpoint of
  FH. IF EG 28, what is EK? GK? FH?
• EK_____ GK_____ FH_____

E
F
K
H
G
10
A

• 7. The mltB 8x26. Find the value of x.
• 8. AC 6x 24, BD 8z 12. Find z. Find
  the length of AC and BD.
• z_____ AC_____ BD_____

B
D
C
11

• PQRS is a rhombus.
• 9. Find the value of y.
• 10. Find the value of x.
• 11. Find the value of z.

P
Q
120º
2y 3
xº
3zº
S
R
5y - 6
12
K
J

• JKLM is a rhombus
• Find the indicated measure.
• 12. JL _____ 13. MT _____
• 14. mltJTK _____ 15. x _____

65º
2n
T
12-n
20
2xº
L
M
13

• TUVW is a Square
• Find the indicated measure.
• 16. p _____ 17. TU ____
• 18. UW _____

4(p3)
T
U
W
V
24
14

• Solve for x and y in the following
  parallelograms.
• 19.
• 20.

a ______ b ______
2a 1
7
2b - 3
21
X ______ Y ______
42º
2xº
7yº
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Homework

• Page 319
• Numbers 7-14
• Page 321
• Numbers 2-22 even