Geometry
Name: _______________________________
Unit 5: Lesson 5.5
Date: _________________ Period: _______
Special Parallelograms (Textbook Section 6.5)
Essential Questions:
 What are common characteristics shared between special parallelograms?
Goal:
 I can understand how to use identify parallelograms that are rhombuses, rectangles, and squares.
Vocabulary/Theorems/Properties:
Rhombus  a parallelogram with four congruent sides.
Rectangle  a parallelogram that has all four right angles.
Square  a parallelogram that has all four right angles and four congruent sides.
Section 1: Describing a Special Parallelogram
1) Decide whether the statement is always,
sometimes, or never true.
Answers:
a.) A square is a rectangle.
__________
b.) A rectangle is a square.
__________
c.) A rhombus is a rectangle. __________
d.) A rhombus is a square.
__________
e.) A parallelogram is a rectangle. __________
f.) A square is equiangular.
__________
YT 1) Name each quadrilateral — parallelogram (P),
rectangle (Rect), rhombus (Rhom), or square (S) —for
which the statement is always true.
Answers:
a.) It is equiangular.
__________
b.) It is equiangular and equilateral. __________
c.) The diagonals are perpendicular. __________
d.) Opposite sides are congruent. __________
e.) The diagonals bisect each other. __________
f.) The diagonals bisect opposite angles. ______
Section 2: Using Properties of Special Parallelograms
2) ABCD is a rhombus. What else do you know about
ABCD?
Answers:





ABCD has four congruent _________.
Its opposite sides are ________.
Its opposite angles are ________.
Its diagonals are ______________.
Its consecutive angles are __________.
YT 2) ABCD is a rectangle. What else do you know
about ABCD?
Answers:





ABCD has four congruent _________.
Its opposite sides are ________ and _________.
Its opposite angles are ________.
Its diagonals __________ and are ________.
Its consecutive angles are __________.
Section 3: Using Properties of Special Parallelograms
3) In the diagram, EFGH is a rectangle. What is the
value of y?
YT 3) In the diagram, QRST is a square. What is the
value of x?
Answer: y = _________
4) In the diagram, PQRS is a rhombus. What is the
value of y and perimeter of PQRS?
Answer: x = _________
YT 4) Find the indicated measures if QRST is a
rectangle.
Answer: y = _________ and Perimeter= __________
5) In the diagram, NPQM is a rhombus. Find the
measure of the numbered angles.
Answers:
YT 5) In the diagram, NPQM is a rhombus. Find the
measure of the numbered angles.
Answer: 1 = ______2 = ______3 = ______4 = _______
6) Find the length of FD in rectangle GFED if
FD = 2y + 4 and GE = 6y – 5.
Answer: 1 = ______2 = ______3 = ______4 = ______
YT 6) Find the length of XZ in rectangle WXYZ if
WY = 24x – 8 and XZ = -18x + 13
Answer: FD = ___________________
Section 4: Coordinate Geometry
7) It is given that PQRS is a quadrilateral. Decide
whether it is a rectangle, a rhombus, a square,
parallelogram, or none of these.
P (5, 2) Q (1, 9) R (-3, 2) S (1, -5)
Answer: XZ = ___________________
Answer:
Section 5: Identifying Special Parallelograms
8) Can you conclude that the parallelogram is a
rhombus or a rectangle?
Answer:
Answer:
Answer:
Homework:
Textbook: Pg. 296 # 1 – 24
Lesson Summary:
YT 7) It is given that PQRS is a quadrilateral. Decide
whether it is a rectangle, a rhombus, a square,
parallelogram, or none of these.
P (0, 8) Q (12, -12) R (32, 0) S (20, 20)
YT 8) Can you conclude that the parallelogram is a
rhombus or a rectangle?