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Quadrilaterals
Parallelogram
Mission:
Determines the conditions
that guarantee a
quadrilateral a
parallelogram
A. Preliminary
In the table that follows, write T in the
second column if your guess on the
statement is true; otherwise, write F. You
are to revisit the same table later on and
respond to your guesses by writing R if you
were right or W if wrong under the third
column.
STATEMENT
My guess is
(T or F)
I was (R or
W)
1. A quadrilateral is a parallelogram if both pairs of
opposite sides are parallel.
2. A quadrilateral is a parallelogram if both pairs of
opposite sides are ≅.
3. A quadrilateral is a parallelogram if both pairs of
opposite angles are ≅.
4. A quadrilateral is a parallelogram if any two
consecutive angles are complementary.
5. A quadrilateral is a parallelogram if exactly one pair
of adjacent sides is perpendicular
6. A quadrilateral is a parallelogram if one pair of
opposite sides are both congruent and parallel
Illustrative Eg.1
In quadrilateral PQRS,
PQ ∥ SR and PS ∥ QR
PQ ≅ SR and PS ≅ QR
∴PQRS is a
parallelogram
IIllustrative Eg. # 2:
In quadrilateral LOVE,
∠L≅ ∠𝑽
∠O≅∠E
∴LOVE is a parallelogram
Illustrative Example # 3:
In quadrilateral HOME, HT≅
MT
and 𝑬𝑻 ≅ 𝑶𝑻
∴HOME is a
parallelogram
Illustrative Example # 4:
m∠C+m∠A=180°
m∠A+m∠R=180°
m∠R+m∠E=180°
m∠E+m∠C=180°
∴CARE is a parallelogram
Illustrative Example # 5
∆HEO≅∆POE
∴HOPE is a parallelogram
Conditions that guarantee a quadrilateral
a parallelogram:
1. Opposite sides of a are ≅
2. Opposite angles of a are ≅
3. Consecutive ∠ of a are
supplementary
4. The diagonals of a bisect each other
5. Either diagonal of a forms two ≅ ∆
What are the conditions
that guarantee that a
quadrilateral is a
parallelogram?
G.1. Alex uses DEFG in completing the table.
REASON
a. EF≅ _____
b. ∠𝑬 ≅ _____
c. 𝑭𝑮 ≅ _____
d. ∆𝑫𝑬𝑭 ≅ _____
e. 𝒎∠𝑫 + 𝒎∠𝑮 = _____
G2-G3.Given: Parallelogram
MATH, find the following:
1. 𝑀𝐴 ≅ ______
2. ∆𝑀𝐴𝐻 ≅ ______
3. 𝑀𝑆 ≅ ______
4. ∆𝑇𝐻𝑀 ≅ ______
5. ∠𝐴𝑇𝐻 ≅ ______
G4-G5. Directions: Complete
the table by illustrating the
parallelogram being described.
Put markings on the figure to
represent the property.
Properties of Parallelogram
Opposite
sides
are parallel
Opposite
sides
are
congruent
Opposite
angles are
congruent
Consecutive
angles are
supplement
ary
Diagonals
bisect each
other
G2
G3
G4-G5
Opposite sides are parallel
Opposite sides are ≅
Opposite angles are ≅
Consecutive ∠are supplementary
Diagonals bisect each other
Exercise #3.2
1.
2.
3.
4.
5.
Ass. #3.2. Directions: Find the values of
x, y, and z in each parallelogram.

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l.2 parallelogram