The document defines and provides examples of different types of angle relationships including adjacent angles, linear pairs, vertical angles, complementary angles, and supplementary angles. It also gives examples of using these concepts to find missing angle measures. For example, if two angles are vertical angles and one is measured as 72 degrees, then the other is also 72 degrees. It also shows how to set up and solve equations to determine missing angle measures or find values that satisfy given conditions, such as finding x and y values so that two lines are perpendicular.
Operation “Blue Star” is the only event in the history of Independent India where the state went into war with its own people. Even after about 40 years it is not clear if it was culmination of states anger over people of the region, a political game of power or start of dictatorial chapter in the democratic setup.
The people of Punjab felt alienated from main stream due to denial of their just demands during a long democratic struggle since independence. As it happen all over the word, it led to militant struggle with great loss of lives of military, police and civilian personnel. Killing of Indira Gandhi and massacre of innocent Sikhs in Delhi and other India cities was also associated with this movement.
2024.06.01 Introducing a competency framework for languag learning materials ...Sandy Millin
http://sandymillin.wordpress.com/iateflwebinar2024
Published classroom materials form the basis of syllabuses, drive teacher professional development, and have a potentially huge influence on learners, teachers and education systems. All teachers also create their own materials, whether a few sentences on a blackboard, a highly-structured fully-realised online course, or anything in between. Despite this, the knowledge and skills needed to create effective language learning materials are rarely part of teacher training, and are mostly learnt by trial and error.
Knowledge and skills frameworks, generally called competency frameworks, for ELT teachers, trainers and managers have existed for a few years now. However, until I created one for my MA dissertation, there wasn’t one drawing together what we need to know and do to be able to effectively produce language learning materials.
This webinar will introduce you to my framework, highlighting the key competencies I identified from my research. It will also show how anybody involved in language teaching (any language, not just English!), teacher training, managing schools or developing language learning materials can benefit from using the framework.
Palestine last event orientationfvgnh .pptxRaedMohamed3
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How to Make a Field invisible in Odoo 17Celine George
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Instructions for Submissions thorugh G- Classroom.pptxJheel Barad
This presentation provides a briefing on how to upload submissions and documents in Google Classroom. It was prepared as part of an orientation for new Sainik School in-service teacher trainees. As a training officer, my goal is to ensure that you are comfortable and proficient with this essential tool for managing assignments and fostering student engagement.
Ethnobotany and Ethnopharmacology:
Ethnobotany in herbal drug evaluation,
Impact of Ethnobotany in traditional medicine,
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Bio-prospecting tools for drug discovery,
Role of Ethnopharmacology in drug evaluation,
Reverse Pharmacology.
Students, digital devices and success - Andreas Schleicher - 27 May 2024..pptxEduSkills OECD
Andreas Schleicher presents at the OECD webinar ‘Digital devices in schools: detrimental distraction or secret to success?’ on 27 May 2024. The presentation was based on findings from PISA 2022 results and the webinar helped launch the PISA in Focus ‘Managing screen time: How to protect and equip students against distraction’ https://www.oecd-ilibrary.org/education/managing-screen-time_7c225af4-en and the OECD Education Policy Perspective ‘Students, digital devices and success’ can be found here - https://oe.cd/il/5yV
The Roman Empire A Historical Colossus.pdfkaushalkr1407
The Roman Empire, a vast and enduring power, stands as one of history's most remarkable civilizations, leaving an indelible imprint on the world. It emerged from the Roman Republic, transitioning into an imperial powerhouse under the leadership of Augustus Caesar in 27 BCE. This transformation marked the beginning of an era defined by unprecedented territorial expansion, architectural marvels, and profound cultural influence.
The empire's roots lie in the city of Rome, founded, according to legend, by Romulus in 753 BCE. Over centuries, Rome evolved from a small settlement to a formidable republic, characterized by a complex political system with elected officials and checks on power. However, internal strife, class conflicts, and military ambitions paved the way for the end of the Republic. Julius Caesar’s dictatorship and subsequent assassination in 44 BCE created a power vacuum, leading to a civil war. Octavian, later Augustus, emerged victorious, heralding the Roman Empire’s birth.
Under Augustus, the empire experienced the Pax Romana, a 200-year period of relative peace and stability. Augustus reformed the military, established efficient administrative systems, and initiated grand construction projects. The empire's borders expanded, encompassing territories from Britain to Egypt and from Spain to the Euphrates. Roman legions, renowned for their discipline and engineering prowess, secured and maintained these vast territories, building roads, fortifications, and cities that facilitated control and integration.
The Roman Empire’s society was hierarchical, with a rigid class system. At the top were the patricians, wealthy elites who held significant political power. Below them were the plebeians, free citizens with limited political influence, and the vast numbers of slaves who formed the backbone of the economy. The family unit was central, governed by the paterfamilias, the male head who held absolute authority.
Culturally, the Romans were eclectic, absorbing and adapting elements from the civilizations they encountered, particularly the Greeks. Roman art, literature, and philosophy reflected this synthesis, creating a rich cultural tapestry. Latin, the Roman language, became the lingua franca of the Western world, influencing numerous modern languages.
Roman architecture and engineering achievements were monumental. They perfected the arch, vault, and dome, constructing enduring structures like the Colosseum, Pantheon, and aqueducts. These engineering marvels not only showcased Roman ingenuity but also served practical purposes, from public entertainment to water supply.
2. Essential Questions
• How do you identify and use special pairs
of angles?
• How do you identify perpendicular lines?
Sunday, September 28, 14
3. Vocabulary
1. Adjacent Angles:
2. Linear Pair:
3. Vertical Angles:
4. Complementary Angles:
Sunday, September 28, 14
4. Vocabulary
1. Ad j a c e n t A n g le s : Two angles that share a vertex and
side but no interior points
2. Linear Pair:
3. Vertical Angles:
4. Complementary Angles:
Sunday, September 28, 14
5. Vocabulary
1. Ad j a c e n t A n g le s : Two angles that share a vertex and
side but no interior points
2. Lin e a r P a ir : A pair of adjacent angles where the non-shared
sides are opposite rays
3. Vertical Angles:
4. Complementary Angles:
Sunday, September 28, 14
6. Vocabulary
1. Ad j a c e n t A n g le s : Two angles that share a vertex and
side but no interior points
2. Lin e a r P a ir : A pair of adjacent angles where the non-shared
sides are opposite rays
3. Ve r t ic a l A n g l e s : Nonadjacent angles that are formed
when two lines intersect; only share a vertex
4. Complementary Angles:
Sunday, September 28, 14
7. Vocabulary
1. Ad j a c e n t A n g le s : Two angles that share a vertex and
side but no interior points
2. Lin e a r P a ir : A pair of adjacent angles where the non-shared
sides are opposite rays
3. Ve r t ic a l A n g l e s : Nonadjacent angles that are formed
when two lines intersect; only share a vertex
4. Co m p l e m e n t a r y A n g le s : Two angles with measures
such that the sum of the angles is 90 degrees
Sunday, September 28, 14
9. Vocabulary
5. Su p p l e m e n t a r y A n g le s : Two angles with measures
such that the sum of the angles is 180 degrees
6. Perpendicular:
Sunday, September 28, 14
10. Vocabulary
5. Su p p l e m e n t a r y A n g le s : Two angles with measures
such that the sum of the angles is 180 degrees
6. Pe r p e n d i c u l a r : When two lines, segments, or rays
intersect at a right angle
Sunday, September 28, 14
21. Example 1
Name a pair that satisfies each condition.
a. A pair of vertical angles
b. A pair of adjacent angles
c. A linear pair
Sunday, September 28, 14
22. Example 1
Name a pair that satisfies each condition.
a. A pair of vertical angles
∠AGF and ∠DGC
b. A pair of adjacent angles
c. A linear pair
Sunday, September 28, 14
23. Example 1
Name a pair that satisfies each condition.
a. A pair of vertical angles
∠AGF and ∠DGC
b. A pair of adjacent angles
∠AGF and ∠FGE
c. A linear pair
Sunday, September 28, 14
24. Example 1
Name a pair that satisfies each condition.
a. A pair of vertical angles
∠AGF and ∠DGC
b. A pair of adjacent angles
∠AGF and ∠FGE
c. A linear pair
∠AGB and ∠BGD
Sunday, September 28, 14
25. Example 1
d. What is the relationship
between the following angles?
∠FGB and ∠BGD
Sunday, September 28, 14
26. Example 1
d. What is the relationship
between the following angles?
∠FGB and ∠BGD
These are adjacent angles
Sunday, September 28, 14
27. Example 2
Find answers to satisfy each condition.
a. Name two complementary
angles
b. Name two supplementary
angles
Sunday, September 28, 14
28. Example 2
Find answers to satisfy each condition.
a. Name two complementary
angles
∠TWU and ∠UWV
b. Name two supplementary
angles
Sunday, September 28, 14
29. Example 2
Find answers to satisfy each condition.
a. Name two complementary
angles
∠TWU and ∠UWV
b. Name two supplementary
angles
∠SWT and ∠TWV
Sunday, September 28, 14
30. Example 2
Find answers to satisfy each condition.
c. If , m∠RWS = 72° find
m∠UWV
d. If m ∠ R W S = 7 2 °, find
m∠RWV
Sunday, September 28, 14
31. Example 2
Find answers to satisfy each condition.
c. If , m∠RWS = 72° find
m∠UWV
m∠UWV = 72°
d. If m ∠ R W S = 7 2 °, find
m∠RWV
Sunday, September 28, 14
32. Example 2
Find answers to satisfy each condition.
c. If , m∠RWS = 72° find
m∠UWV
m∠UWV = 72°
(vertical angles)
d. If m ∠ R W S = 7 2 °, find
m∠RWV
Sunday, September 28, 14
33. Example 2
Find answers to satisfy each condition.
c. If , m∠RWS = 72° find
m∠UWV
m∠UWV = 72°
(vertical angles)
d. If m ∠ R W S = 7 2 °, find
m∠RWV
180° − 72°
Sunday, September 28, 14
34. Example 2
Find answers to satisfy each condition.
c. If , m∠RWS = 72° find
m∠UWV
m∠UWV = 72°
(vertical angles)
d. If m ∠ R W S = 7 2 °, find
m∠RWV =108°
m∠RWV
180° − 72°
Sunday, September 28, 14
35. Example 2
Find answers to satisfy each condition.
c. If , m∠RWS = 72° find
m∠UWV
m∠UWV = 72°
(vertical angles)
d. If m ∠ R W S = 7 2 °, find
m∠RWV =108°
m∠RWV
(supplementary angles)
180° − 72°
Sunday, September 28, 14
36. Example 2
Find answers to satisfy each condition.
e. Name two
perpendicular segments
f. If , m∠UWV = 47° find
m∠UWT
Sunday, September 28, 14
37. Example 2
Find answers to satisfy each condition.
e. Name two
perpendicular segments
SW and TW
f. If , m∠UWV = 47° find
m∠UWT
Sunday, September 28, 14
38. Example 2
Find answers to satisfy each condition.
e. Name two
perpendicular segments
SW and TW
f. If , m∠UWV = 47° find
m∠UWT
90° − 47°
Sunday, September 28, 14
39. Example 2
Find answers to satisfy each condition.
e. Name two
perpendicular segments
SW and TW
f. If , m∠UWV = 47° find
m∠UWT = 43°
m∠UWT
90° − 47°
Sunday, September 28, 14
40. Example 2
Find answers to satisfy each condition.
e. Name two
perpendicular segments
SW and TW
f. If , m∠UWV = 47° find
m∠UWT = 43°
m∠UWT
(complementary angles)
90° − 47°
Sunday, September 28, 14
41. Example 3
Find x and y so that AE ⊥ CF .
Sunday, September 28, 14
42. Example 3
Find x and y so that AE ⊥ CF .
2x + 14 + 2x = 90
Sunday, September 28, 14
43. Example 3
Find x and y so that AE ⊥ CF .
2x + 14 + 2x = 90
4x + 14 = 90
Sunday, September 28, 14
44. Example 3
Find x and y so that AE ⊥ CF .
2x + 14 + 2x = 90
4x + 14 = 90
−14 −14
Sunday, September 28, 14
45. Example 3
Find x and y so that AE ⊥ CF .
2x + 14 + 2x = 90
4x + 14 = 90
−14 −14
4x = 76
Sunday, September 28, 14
46. Example 3
Find x and y so that AE ⊥ CF .
2x + 14 + 2x = 90
4x + 14 = 90
−14 −14
4x = 76
4 4
Sunday, September 28, 14
47. Example 3
Find x and y so that AE ⊥ CF .
2x + 14 + 2x = 90
4x + 14 = 90
−14 −14
4x = 76
4 4
x = 19
Sunday, September 28, 14
48. Example 3
Find x and y so that AE ⊥ CF .
2x + 14 + 2x = 90
4x + 14 = 90
−14 −14
4x = 76
4 4
x = 19
8y + 10 = 90
Sunday, September 28, 14
49. Example 3
Find x and y so that AE ⊥ CF .
2x + 14 + 2x = 90
4x + 14 = 90
−14 −14
4x = 76
4 4
x = 19
8y + 10 = 90
−10 −10
Sunday, September 28, 14
50. Example 3
Find x and y so that AE ⊥ CF .
2x + 14 + 2x = 90
4x + 14 = 90
−14 −14
4x = 76
4 4
x = 19
8y + 10 = 90
−10 −10
8y = 80
Sunday, September 28, 14
51. Example 3
Find x and y so that AE ⊥ CF .
2x + 14 + 2x = 90
4x + 14 = 90
−14 −14
4x = 76
4 4
x = 19
8y + 10 = 90
−10 −10
8y = 80
8 8
Sunday, September 28, 14
52. Example 3
Find x and y so that AE ⊥ CF .
2x + 14 + 2x = 90
4x + 14 = 90
−14 −14
4x = 76
4 4
x = 19
8y + 10 = 90
−10 −10
8y = 80
8 8
y = 10
Sunday, September 28, 14
53. Example 4
Find the measures of two supplementary angles so that
the difference between the measures of the two angles
is 44.
x° (180 − x)°
Sunday, September 28, 14
54. Example 4
Find the measures of two supplementary angles so that
the difference between the measures of the two angles
is 44.
x° (180 − x)°
(180 − x) − x = 44
Sunday, September 28, 14
55. Example 4
Find the measures of two supplementary angles so that
the difference between the measures of the two angles
is 44.
x° (180 − x)°
(180 − x) − x = 44
180 − 2x = 44
Sunday, September 28, 14
56. Example 4
Find the measures of two supplementary angles so that
the difference between the measures of the two angles
is 44.
x° (180 − x)°
(180 − x) − x = 44
180 − 2x = 44
−180 −180
Sunday, September 28, 14
57. Example 4
Find the measures of two supplementary angles so that
the difference between the measures of the two angles
is 44.
x° (180 − x)°
(180 − x) − x = 44
180 − 2x = 44
−180 −180
−2x = −136
Sunday, September 28, 14
58. Example 4
Find the measures of two supplementary angles so that
the difference between the measures of the two angles
is 44.
x° (180 − x)°
(180 − x) − x = 44
180 − 2x = 44
−180 −180
−2x = −136
−2 −2
Sunday, September 28, 14
59. Example 4
Find the measures of two supplementary angles so that
the difference between the measures of the two angles
is 44.
x° (180 − x)°
(180 − x) − x = 44
180 − 2x = 44
−180 −180
−2x = −136
−2 −2
x = 68°
Sunday, September 28, 14
60. Example 4
Find the measures of two supplementary angles so that
the difference between the measures of the two angles
is 44.
x° (180 − x)°
(180 − x) − x = 44
180 − 2x = 44
−180 −180
−2x = −136
−2 −2
x = 68°
180 − 68
Sunday, September 28, 14
61. Example 4
Find the measures of two supplementary angles so that
the difference between the measures of the two angles
is 44.
x° (180 − x)°
(180 − x) − x = 44
180 − 2x = 44
−180 −180
−2x = −136
−2 −2
x = 68°
180 − 68 =112°
Sunday, September 28, 14
62. Example 4
Find the measures of two supplementary angles so that
the difference between the measures of the two angles
is 44.
x° (180 − x)°
(180 − x) − x = 44
180 − 2x = 44
−180 −180
−2x = −136
−2 −2
x = 68°
180 − 68 =112°
The two angles are 68°
and 112°
Sunday, September 28, 14
