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Republic of the Philippines
Department of Education
Regional Office IX, Zamboanga Peninsula
Mathematics
Quarter 3 - Module 1:
PARALLELOGRAMS
Z est for P rogress Z eal of P artnership
Name of Learner: ___________________________
Grade & Section: ___________________________
Name of School: ___________________________
H
E M
O
What I Need to Know
LEARNING COMPETENCIES
In this module, you will be able to:
a. review quadrilaterals and its related terms; b. determine the conditions that make a quadrilateral a parallelogram; and c. uses properties to find measures of angles, sides and other quantities involving parallelograms.
What I Know
Find out how much you already know about this lesson. Encircle the letter of the correct answer. Take note of the items that you were not able to answer correctly and find out the right answer as you go through this module.
- Which quadrilateral has two pairs of parallel sides? a. parallelogram b. square c. rectangle d. rhombus
- Which parallelogram has four right angles? a. parallelogram b. square c. rectangle d. rhombus
- Which rectangle has four congruent sides? a. parallelogram b. square c. rectangle d. rhombus
- Which quadrilateral has exactly one pair of parallel sides? a. parallelogram b. square c. rectangle d. rhombus
- Which parallelogram has four congruent sides? a. parallelogram b. quadrilateral c. rectangle d. rhombus
- Two consecutive angles of a parallelogram have measures (x + 30)˚ and [2(x – 30)]˚. What is the measure of the smaller angle? a. 30˚ b. 80˚ c. 100˚ d. 140˚ 7.What is true about any two consecutive angles in a parallelogram? a. They are always congruent. b. They are always supplementary. c. They are sometimes complementary. d. They are always right angles. 8.Which of the following properties is NOT sufficient to prove that a quadrilateral is a parallelogram? a. Two pairs of sides are parallel. b. Two pairs of opposite sides are congruent. c. Two angles are supplementary. d. Two diagonals bisect each other.
- Which of the following parallelograms has diagonals that do not bisect each other? a. Square b. Rhombus c. Rectangle d. Trapezoid 10.What is the measure of M in rhombus HOME? a. 75˚ b. 90˚ c. 105˚ d. 180˚
105˚
What’s New
ACTIVITY 1: PARALLELOGRAM OR NOT A PARALLELOGRAM
Directions: Identify whether the following are parallelograms or not. Put a check mark ( √ ) under the appropriate column.
QUADRILATERAL PARALLELOGRAM NOT A PARALLELOGRAM
1. TRAPEZOID
2. RECTANGLE
3. RHOMBUS
4. SQUARE
ACTIVITY 1.1: NAME IT!
Directions: Given the figure below, give what is/are asked in each number.
D C
A B
Quadrilateral ABCD is a parallelogram.
- Name two pairs of congruent sides.
- Name two pairs of congruent angles.
- Name two pairs of supplementary angles.
- Name the diagonals.
- Name the two triangles formed by diagonal AC
- Name the two triangles formed by diagonal BD
67° 113°
What is it
Focus Discussion 1: CONDITIONS WHICH GUARANTEE THAT A QUADRILATERAL A PARALLELOGRAM
FIGURE
CONDITIONS THAT GUARANTEE THAT
A QUADRILATERAL A
PARALLELOGRAM
- A quadrilateral is a parallelogram if both pairs of opposite sides are congruent.
- A quadrilateral is a parallelogram if both pairs of opposite angles are congruent.
- A quadrilateral is a parallelogram if pairs of consecutive angles are supplementary.
- A quadrilateral is a parallelogram if the diagonals bisect each other.
- A quadrilateral is a parallelogram if one pair of opposite sides are congruent and parallel.
- A quadrilateral is a parallelogram if each diagonal divides a parallelogram into two congruent triangles.
Focus Discussion 2: PROPERTIES OF PARALLELOGRAM Using the properties of parallelogram, we can now identify how quadrilaterals are considered parallelogram.
H E
O R
6 6
5
5
113°^ 67°
115°
65°^ 115°
65°
Given:.
What is the value of x?
CD = EF
- write the correct equation
- addition property of equality
How long is CD?
- measure of side CD
- substitution
- simplify CD =8cm
what is the value of y?
CF = DE
(y+3)cm=(2y-7)cm y+
How long is CF?
- measure of side CF
- substitution method
- simplify
Given: Diagonals CE and DF meet at G. FG is 8cm and CE is 13cm.
How long is DF?
Since the measure of FG=8cm which is half the measure of the diagonal DF. Therefore, the measure of DF=16cm.
How long is CG?
Since the measure of CE=13, and CG is half the measure of CE, therefore the measure of CG=6.5cm.
What’s More
Acrivity 2: Math is Fun!
A. Refer to the given figure at the right and answer the following.
Given. MATH is a parallelogram.
1. MA ________
2. MAH _________
3. MS _________
4. ∆ THM ________
5. ATH _________
- If m MHT= 100, then m MAT ____________
- If m AMH =100, then m MHT ___________
- If MH = 7, then AT= ____________
- If AS = 3, then AH = _____________ 10.If MT = 9, then SM = ______________
B. Put a check ( √ ) mark in the table to which the property corresponds to the given quadrilateral.
Property
Quadrilaterals Parallel
- ogram
Rectangle Rhombus Square
- All sides are congruent
- Opposite sides are parallel.
- Opposite sides are congruent.
- Opposite angles are congruent.
- Opposite angles are supplementary.
- Diagonals are congruent.
- Diagonals bisect each other.
- Diagonals bisect opposite angles.
- Diagonals are perpendicular to each other.
- A diagonal divides a quadrilateral into two congruent s.
M
H
T
A S
Assessment
Directions: Encircle the letter of the correct answer.
- Which angle of a parallelogram are consecutive angles? a. adjacent b. complementary c. congruent d. supplementary
- What do you call a quadrilateral with exactly one pair of parallel sides? a. rectangle b. rhombus c. square d. trapezoid
- The figure below is a parallelogram ABCD. If AD=2x-10 and BC=x+30.
What is Segment BC?
a. 50 D C b. 60 c. 70 d. 80 A B
- The figure below is a rhombus GIVE. If m I=(4x)^0 and m E=(2x+60)^0.
what is the measure of angle I?
a. 100^0 E V b. 110^0 c. 120^0 d. 130^0 G I
- Quadrilateral BEST is a parallelogram, If m B=(x+40)^0 and m E=(2x+20)^0.
what is the measure of angle B?
a. 50^0 T S b. 60^0 c. 70^0 d. 80^0 B E
ES= 12b + 1 SO= 2b + 21 Find SO
- The figure below is a parallelogram. The diagonals AC and BD intersect at E. If AE=2x and EC 12.
what is the value of x? a. x=5 D C b. x= c. x= d. x=8 A B
- How many congruent triangles are formed when a diagonal of a parallelogram is drawn? a. 1 b. 2 c. 3 d. 4
- Which is NOT a properties of a parallelogram? a. diagonals bisect each other c. opposite angles are congruent b. opposite sides are congruent d. opposite sides are not parallel
- Which statement ensures that a quadrilateral is a parallelogram? a. diagonals bisect each other b. two diagonals are congruent c. two consecutive sides are congruent d. two consecutive angles are congruent
- The diagonals of a rectangle ABCD, BD=5x-11 and CD=2x +25.
What is the length of each diagonal? a. 12 b. 24 c. 49 d. 60
E
D. Put a check ( √ ) mark in the table to which the property corresponds to the given quadrilateral.
Property
Quadrilaterals Parallelo gram
Rectangle Rhombu s
Square
- All sides are congruent √ √
- Opposite sides are parallel. √ √ √ √
- Opposite sides are congruent. √ √ √ √
- Opposite angles are congruent. √ √ √ √
- Opposite angles are supplementary. √ √
- Diagonals are congruent. √ √
- Diagonals bisect each other. √ √ √ √
- Diagonals bisect opposite angles. √ √
- Diagonals are perpendicular to each other. √ √
- A diagonal divides a quadrilateral into two congruent s.
What I Can Do Try to answer the following to check if you are ready for the assessment.
1. LO = 10
2. VEL = 130^0
- m ELO= 45^0 and m LOV= 135^0
- LS= 35
- SO= 25
Assessment
- d
- d
- c
- c
- d
- b
- b
- d
- a
- c
References
Bryant, Merden L., Leonides E. Bulalayao, Melvin M. Callanta, Jerry D. Cruz, et al. the ti s Le r er’s Material 9. Pasig City: Department of Education, 2014.
Bryant, Merden L., Leonides E. Bulalayao, Melvin M. Callanta, Jerry D. Cruz, et al.Mathematics Teachers Guide 9. Pasig City: Department of Education, 2014
Bernabe, Julieta G., Soledad Jose-Dilao and Fernando B Orines, Quadrilaterals Geometry, 1251 Gregorio Araneta Avenue, Quezon City: SD Publications Inc., 2009.
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Surabay National High School
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