This document discusses properties of quadrilaterals including parallelograms, rectangles, rhombuses, and squares. It provides definitions and key properties of each shape. Students are instructed to create a foldable study guide defining and comparing the different quadrilaterals. They will draw examples of each and list their distinguishing properties. The document aims to help students learn the different theorems and identify the characteristics that define special types of parallelograms.

1. Grade 9 Mathematics
Search for
classpoint.app
And type in the code

2. Identify the different theorems of
rectangle, rhombus and square.
 Apply the different theorems of
rectangle, rhombus and square in
finding their unknown parts and in real-
life situations.

3.  Let me check your attendance by showing me how you
are feeling today.
 Draw the emoji on how your group is feeling today in the
box below.
 And explain why.

4.  Tell me whether the given illustrations
shows enough information to prove
that a quadrilateral is a parallelogram.
 Just answer yes or no.

5. 
60 
120

120
6 6

6. 50°
130°

7. What are the different theorems of rectangle.
Rhombus and square?

8.  The three special types of parallelograms:
rhombuses, rectangles and squares.
A rhombus is a parallelogram
with four congruent sides
A rectangle is a parallelogram
with four right angles.
A square is a parallelogram
with four congruent sides
and four right angles.

11. Some examples of a rhombus

12.  In the diagram at the right,
PQRS is a rhombus. What
is the value of y?
All four sides of a rhombus are ≅, so RS = PS.
5y – 6 = 2y + 3 Equate lengths of ≅ sides.
5y = 2y + 9 Add 6 to each side.
3y = 9 Subtract 2y from each side.
y = 3 Divide each side by 3.
5y - 6
2y + 3
P
S
Q
R

13.  Theorem 1: A
parallelogram is a
rhombus if and only if
its diagonals are
perpendicular.
 ABCD is a rhombus if
and only if AC BD.

14.  Theorem 2: A
parallelogram is a
rhombus if and only if
each diagonal bisects a
pair of opposite angles.
 ABCD is a rhombus if
and only if AC bisects
DAB and BCD and
BD bisects ADC and
CBA.

17. 
A B
C
D

18.  Theorem 4: A
parallelogram is a
rectangle if and only if
its diagonals are
congruent.
 ABCD is a rectangle if
and only if AC ≅ BD.
A B
C
D

22. Characteristics P Re Rh S
Both pairs of opposite sides parallel
Diagonals are congruent
Both pairs of opposite sides congruent
At least one right angle
Both pairs of opposite angles congruent
Exactly one pair of opposite sides parallel
Diagonals are perpendicular
All sides are congruent
Consecutive angles congruent
Diagonals bisect each other
Diagonals bisect opposite angles
Consecutive angles supplementary

23. 1. Take out a piece
of notebook paper
and make a hot
dog fold over from
the right side over
to the pink line.

24. 2. Now, divide the right
hand section into 5
sections by drawing 4
evenly spaced lines.
The fold crease
3. Use scissors to cut
along your drawn line,
but ONLY to the crease!

25. 4. Write
QUADRILATERALS
down the left hand
side
The fold
crease

26. 5. Fold over the top
cut section and write
PARALLELOGRAM
on the outside.
The fold
crease
6. Reopen the fold.

27. 7. On the left hand
section, draw a
parallelogram.
1. Opposite angles are congruent.
2. Consecutive angles are
supplementary.
3. Opposite sides are congruent.
4. Diagonals bisect each other.
5. Opposite sides are parallel
8. On the right hand
side, list all of the
properties of a
parallelogram.

28. * Fold over the
second cut section
and write
RECTANGLE on the
outside.
* Reopen the fold.
1. Opposite angles are congruent.
2. Consecutive angles are
supplementary.
3. Opposite sides are congruent.
4. Diagonals bisect each other.
5. Opposite sides are parallel

29. * On the left hand
section, draw a
rectangle.
1. Opposite angles are congruent.
2. Consecutive angles are
supplementary.
3. Opposite sides are congruent.
4. Diagonals bisect each other.
5. Opposite sides are parallel
* On the right hand
side, list all of the
properties of a
rectangle.
1. Special parallelogram.
2. Has 4 right angles
3. Diagonals are congruent.

30. * Fold over the third
cut section and write
RHOMBUS on the
outside.
* Reopen the fold.
1. Opposite angles are congruent.
2. Consecutive angles are
supplementary.
3. Opposite sides are congruent.
4. Diagonals bisect each other.
5. Opposite sides are parallel
1. Special parallelogram.
2. Has 4 right angles
3. Diagonals are congruent.

31. * On the left hand
section, draw a
rhombus.
1. Opposite angles are congruent.
2. Consecutive angles are
supplementary.
3. Opposite sides are congruent.
4. Diagonals bisect each other.
5. Opposite sides are parallel
* On the right hand
side, list all of the
properties of a
rhombus.
1. Special parallelogram.
2. Has 4 right angles
3. Diagonals are congruent.
1. Special Parallelogram
2. Has 4 Congruent sides
3. Diagonals are perpendicular.
4. Diagonals bisect opposite angles

32. * Fold over the third
cut section and write
SQUARE on the
outside.
* Reopen the fold.
1. Opposite angles are congruent.
2. Consecutive angles are
supplementary.
3. Opposite sides are congruent.
4. Diagonals bisect each other.
5. Opposite sides are parallel
1. Special parallelogram.
2. Has 4 right angles
3. Diagonals are congruent.
1. Special Parallelogram
2. Has 4 Congruent sides
3. Diagonals are perpendicular.
4. Diagonals bisect opposite angles

33. * On the left hand
section, draw a
square.
1. Opposite angles are congruent.
2. Consecutive angles are
supplementary.
3. Opposite sides are congruent.
4. Diagonals bisect each other.
5. Opposite sides are parallel
* On the right hand
side, list all of the
properties of a
square.
* Place in your
notebook and save
for tomorrow.
1. Special parallelogram.
2. Has 4 right angles
3. Diagonals are congruent.
1. Special Parallelogram
2. Has 4 Congruent sides
3. Diagonals are perpendicular.
4. Diagonals bisect opposite angles
1. All the properties of parallelogram,
rectangle, and rhombus
2. 4 congruent sides and 4 right
angles

34.  CARPENTRY. You are
building a rectangular
frame for your Bulletin
Board.
a. First, you nail four pieces
of wood together as shown
at the right. What is the
shape of the frame?
b. To make sure the frame is
a rectangle, you measure
the diagonals. One is 7
feet 4 inches. The other is
7 feet 2 inches. Is the
frame a rectangle?
Explain.
4 feet
4 feet
6 feet 6 feet