Properties of Special Parallelograms
section 6-4
Besides the parallelogram, another special
quadrilateral is a rectangle. A rectangle is a
quadrilateral with four right angles.
Since a rectangle is a parallelogram by Theorem 6-4-1, a rectangle “inherits”
all the properties of parallelograms that you learned in Lesson 6-2.
problem # 1 - A woodworker constructs a rectangular picture frame so that JK = 50 cm
and JL = 86 cm. Find HM.
problem # 2 - The rectangular gate shown has diagonal braces. Find HJ and HK.
H
J
L
G
30.8 in.
48 in. K
A rhombus is another special
quadrilateral. A rhombus is a
quadrilateral with four congruent sides.
Like a rectangle, a rhombus is a parallelogram. So you can apply the properties
of parallelograms to rhombuses.
problem # 3 - RSTV is a rhombus. Find each measure.
4x + 7
S
a. VT
T
W
9x - 11
V
R
S
b. m
T
(y + 2)
(2y + 10)
WSR
W
V
R
A square is a quadrilateral with four right angles and
four congruent sides. A square is also a parallelogram,
a rectangle, and a rhombus. So a square has the
properties of all three.
Venn diagram - a diagram using geometric figures to show the relationships
between different sets of objects
Quadrilaterals
parallelograms
Rectangles
Squares
Rhombuses
** Any property that belongs to one of the bigger sets also belongs to each
smaller subset within it. The opposite is NOT true.
problem # 4 - Show that the diagonals of
square EFGH are congruent
perpendicular bisectors of
each other.
problem # 5 - Complete the following proof.
Given: EFGH is a rectangle. J is the midpoint of EH.
Prove:
FJG is isosceles.
G
F
E
1. EFGH is a rectangle; J is the
midpt. of EH
2. E and H are right angles
3.
E
J
1.
2.
3.
H
4. EFGH is a parallelogram
4.
5. EF
HG
5.
6. EJ
HJ
7.
FJE
8. FJ
9.
H
6.
GJH
GJ
7.
8.
FJG is isosceles
9.
** Real-life applications of the rhombus - car jack, security gate, & trolley wires
(see the next page for pictures)
Rhombus Application - Car Jack
Rhombus Application - Trolley Wires
Rhombus Application - Security Gate