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Lesson 2 – Angle formed by parallel lines cut by a transversal ... 11. ANSWER KEY. GRADE 7 MATHEMATICS. Quarter 3 Module 2. WHAT I KNOW! 1. A. 2. B.
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Department of Education
Z est for P rogress Z eal of P artnership
Name of Learner: ___________________________
Grade & Section: ___________________________
Name of School: ___________________________
This module contains two lessons:
For item number 5 to 6, given the lines x and y and the line t is a transversal of the two lines
What I Need to Know
Lesson 1 – On Angle Pairs Lesson 2 – Angle formed by parallel lines cut by a transversal After going through this module, you are expected to: a. Define angle pairs and different types of angles; b. Classify angles according to their measure; and c. Determine the measure of the angles using relationships between angle pairs and angles formed by parallel lines cut by a transversal.
What I Know
Directions: Choose the letter of the best answer. Write the chosen letter on the space provided for you. _____ 1.) Which term describes as two angles are coplanar, have common vertex and a common side but have no common interior points? A. Adjacent angles B. Congruent angles C. Vertical angles D. Obtuse angles _____ 2.) Which statements below define parallel lines? A. They are coplanar, have common vertex and a common side. B. Coplanar lines that do not intersect. C. The angles are congruent D. The sum of the two angles is 180^0
_____ 3.) What is the measure of the angle marked with letter f? Use the figure on the right side_. f_ A. 280 B. 38^0 C.48^0 D. 58^0
_____ 4.) How many degrees needed to complete the rotation if a = 40^0 , b = 30^0 , c = 80^0? Use the figure on the right side. A. 200 B. 30^0 C. 40^0 D.50^0
_____5.) What is the value of d , if C = (3d – 8)^0 and B = (2d + 17)^0? A. 150 B. 25^0 C.35^0 D.45^0
a b
c
t
A B=80^0 C (^) D E (^) F=80 0 G (^) H
x
y
Column A Column B 1.) m DKE = _____ G = 115 2.) m MKE = _____ A = 30 3.) m OKE = _____ N = 70 4.) m RKE = _____ E = 85 5.) m OKD = _____ L = 170 What is the message from the king? Answer: ___ ___ ___ ___ ___
What’s New
Activity 2: Fill Me! Directions: Fill in the best answer on the space provided. 1.) If <R is right angle, what is the possible R (2j – 10) value of j? Ans:___________ 2.) In the figure, what is the relationship a=50^0 b=50^0 Between a and b? Ans: ____________ Activity 3: TESSELATIONS! Directions: Based on the pictures given below, write your observation on the space provided.
0
30
D
70
90 115
150
170
K
(^180) E
M
N O
P
R
S
What Is It
Definitions: 1.) Two angles are adjacen t if they are coplanar, have common vertex and a common interior points. 2.) Two angles are complementary if the sum of their measures is 90^0. 3.) Two angles are supplementary if the sum of their measures is 180^0. 4.) Two angles form a linear pair if they are both adjacent and supplementary. 5.) Vertical angles are congruent. 6.) Vertical angles are the opposite angles formed when two lines intersect 7.) If two lines or segments intersect so that they form a right angle, then they are perpendicular. 8.) Parallel lines are coplanar lines that do not intersect. 9.) Inductive reasoning uses specific examples to arrive at a general rule, generalizations, or conclusions.
Activities 4: JUSTIFY IT! Directions: Answer the empty space and use inductive reasoning to justify your answer. For item 1 and 2, Use the figure to identify the following:
1.) What is the common vertex and side of NOQ? Answer: _____________ and ____________ 2.) What is the relationship between NOP and POQ? Answer: ___________________ 3.) What is the m NOQ, if m RON = 130^0? Answer: ________ 4.) How is NOQ and RON related? Answer: _________________________________ 5.) What are the two perpendicular lines, given m MOQ = 90^0? Answer: _____& ____ ANGLE FORMED BY PARALLEL LINES CUT BY A TRANSVERSAL Discussion: 1.) Two lines are parallel if and only if they are coplanar and they do not intersect. ( p II q )
Transversal
p
q
f 1 2 (^3 )
(^5 ) (^7 )
5.) Determine whether the statement is true or false. If false, explain why? a. 500 100 300 are complementary angles b. 1200 400 200 are supplementary angles
Activity 6: KNOW ME!
Directions: Complete the table below using the given figure as your reference:
What I Have Learned
Activities 7: FILL MY MISSING PART! Directions : Fill in the black or missing part to make the statement true. Use the word/s in a box that corresponds to the black or missing part in the statement.
1.) A ____________ is a line that intersects two or more parallel lines. 2.) Two angles are ______________ if they are coplanar, have common vertex and a common interior points.
Corresponding Angles
Alternate Interior Angles
Alternate Exterior Angles
Same Side Interior Angles
Same Side Exterior Angles
a
b
1 2 (^34)
(^5 ) 7 8
Adjacent Complementary Supplementary Linear pair Vertical angles
Perpendicular Parallel lines Congruent Transversal Inductive reasoning
k
As we observed in our environment geometric figures, parallel lines, and angles are everywhere. Football field, roads, edges of tables, doors, fence, etc. relates geometric figures, parallel lines, and angles. Name angle pairs formed by two parallel lines cut by by a transversal.
3.) Two angles are _______________ if the sum of their measures is 90^0. 4.) Two angles are _______________ if the sum of their measures is 180^0. 5.) Two angles form a ______________ if they are both adjacent and supplementary. 6.) Vertical angles are _______________. 7.) ________________ are the opposite angles formed when two lines intersect 8.) If two lines or segments intersect so that they form a right angle, then they are _______________. 9.) _______________ are coplanar lines that do not intersect. 10.) __________________ uses specific examples to arrive at a general rule, generalizations, or conclusions.
Activity 8: LET’S INVESTIGATE! Two parallel lines when cut by a transversal form eight angles. This activity will lead you to investigate the relationship between the angles formed. Directions: Measure the eight angles using your protractor and list all inferences or observations in the activity. OBSERVATIONS:
m<1 = ____ ___________________________ m<2 = ____ ___________________________ m<3 = ____ ___________________________ m<4 = ____ ___________________________ m<5 = ____ ___________________________ m<6 = ____ ___________________________ m<7 = ____ ___________________________ m<8 = ____ ___________________________
Questions: 1.) What pairs of angles have equal measures?
2.) What pairs of angles are supplementary?
3.) What are the names of the pairs of angles formed when cut by a transversal?
4.) How are the pairs of angles formed when cut by a transversal related?
1 2 (^34)
(^5 ) 7 8
For item number 5 and 6, use the figure on the right.
impact of the project is highly impressive and the use of technology is highly commendable
impact of the project is impressive and the use of technology is commendable
impact of the project is fair and the use of technology is evident.
impact of the project is poor and the use of technology is not evident
Efficiency
The miniature is 90% - 100% functional and flawlessly done
The miniature is 80%-89% functional and flawless.
The miniature is 70%-79% functional.
The miniature is 50%-69% functional.
Mathematical Justification
Justification is logically clear, convincing, and the concepts of angle pairs and parallel lines are applied
Justification is clear, convincing, and the concepts of angle pairs and parallel lines are applied
Justification is not so clear. The concepts of angle pairs and parallel lines are 50% applied
Justification is ambiguous. The concepts of angle pairs and parallel lines are below 49% applied
Assessment
Directions : Choose the letter of the best answer. Write the chosen letter on the space provided for you. _____ 1.) Which of the statements below is always true? A. Lines that intersect are parallel lines B. Coplanar lines that do not intersect are parallel lines C. Lines that form right angle are parallel lines D. Skew lines are parallel lines _____ 2.) What is the supplement of an angle if the given angle measures 135^0? A. 450 B. 55^0 C. 65^0 D.75^0 _____ 3.) What is the measure of the angle marked with letter g? Use the figure on the right side_._ A. 470 B. 57^0 C.67^0 D. 87^0 _____ 4.) Which of the pairs of angles guarantees that q // r?
_____5.) What is the value of d , if C = (4d – 8)^0 and D = (2d + 18)^0? A. 130 B. 26^0 C.36^0 D.46^0
g
1 3
2 4 5 6 7 8
x
y
C=60^0 D (^) E F (^) G=60 0 H (^) I
B
k
q
r
You are a senior scout leader. You want to make a tree guard for the school tree planting. Your senior scout members suggested four different layouts for the design.
A. Because the two angles are exterior angles and they are congruent B. Because the two angles are alternate interior angles and they are congruent C. Because the two angles are alternate exterior angles they are congruent D. Because the two angles are corresponding angles and they are congruent _____7.) What is the value of x, if 1 = (2x + 20)^0 and 2 = (m + 130)^0. A. 50 B. 100 C. 150 D. 250 _____8.) What is the measure of 3 if m 1 = 85^0 and the given parallel lines s and t are cut by a transversal l? A. 50 B. 850 C. 950 D. 2750 _____9.) Which angles are congruent to 5, use the given parallel lines m and n cut by a transversal k? A. 1, 2, and 3 B. 1, 4 and 8 C. 1, 4 and 7 D. 1, 2 and 8
_____10.) Which of the layouts below will you make to ensure stability?
A. C
1 2 3 4
7
(^5 ) 8
s
t
(^1 ) 3 4
7
5 6 8
m
n
k
l
(^1 ) (^3 )
7
(^5 ) 8
q
r
s
12
Activity 5 KNOW ME! Corresponding angles ( <1 and <5, <2 and <6, <3 and <7, <4 and <8) Alternate interior angles (<3 and <6, <4 and <5) Alternate exterior angles (<1 and <8, <2 and <7) Interior angles on the same side of the transversal (<3 and <5, <4 and <6) Exterior angles on the same side of the transversal(<1 and <7, <2 and <8) WHAT I HAVE LEARNED! ACTIVITY 6 1.) Transversal 2.) Adjacent 3.) Complementary 4.) Supplementary 5.) Linear pair 6.) Congruent 7.) Vertical angles 8.) Perpendicular 9.) Parallel lines 10.) Inductive reasoning ACTIVITY 7 Two parallel lines when cut by a transversal form eight angles. This activity will lead you to investigate the relationship between the angles formed. Measure the eight angles using your protractor and list all inferences or observations in the activity. OBSERVATIONS: m<1 = ____ Answers’ here may vary m<2 = ____ ___________________________ m<3 = ____ ___________________________ m<4 = ____ ___________________________ m<5 = ____ ___________________________ m<6 = ____ ___________________________ m<7 = ____ ___________________________ m<8 = ____ ___________________________ Questions: 1.) What pairs of angles have equal measures? ( <1 and <5, <2 and <6, <3 and <7, <4 and <8) (<3 and <6, <4 and <5), (<1 and <8, <2 and <7) 2.) What pairs of angles are supplementary? (<3 and <5, <4 and <6), (<1 and <7, <2 and <8 ) 3.) What are the names of the pairs of angles formed when cut by a transversal? Corresponding angles Alternate interior angles Alternate exterior angles Interior angles on the same side of the transversal Exterior angles on the same side of the transversal 4.) How are the pairs of angles formed when cut by a transversal related?
( <1 and <5, <2 and <6, <3 and <7, <4 and <8) (<3 and <6, <4 and <5) (<1 and <8, <2 and <7) (<3 and <5, <4 and <6)
Use the rubric in giving rate to the students output. ASSESSMENT
Prepared by:
ROMEL S. FLORES
