This document provides a lesson on similar figures and proportions. It begins with warm up problems comparing ratios to determine if they are equal. It then presents a problem of the day involving finding the first telephone pole with both a red band and emergency call phone. The lesson presentation section defines similar figures as those with the same shape but not necessarily the same size, and having equal corresponding angles and proportional corresponding sides. It provides examples of determining if triangles and four-sided figures are similar by setting up ratios of corresponding sides. The document concludes with a two-part lesson quiz involving identifying if given figures are similar.
This powerpoint presentation is an introduction for the topic TRIANGLE CONGRUENCE. This topic is in Grade 8 Mathematics. I hope that you will learn something from this sides.
This powerpoint presentation is an introduction for the topic TRIANGLE CONGRUENCE. This topic is in Grade 8 Mathematics. I hope that you will learn something from this sides.
Parallelogram is a quadrilateral with two pairs of parallel sides.
There are 6 properties of parallelogram.
1. A diagonal of a parallelogram divides it into two congruent triangles.
2. Opposites sides of a parallelogram are congruent.
3. Opposite angles of a parallelogram are congruent.
4. Consecutive angles of a parallelogram are supplementary.
5. If one angle in a parallelogram is right, then all angles are right.
6. The diagonals of a parallelogram bisect each other.
Prove and apply properties of rectangles, rhombuses, and squares.
Use properties of rectangles, rhombuses, and squares to solve problems.
Prove that a given quadrilateral is a rectangle, rhombus, or square.
Parallelogram is a quadrilateral with two pairs of parallel sides.
There are 6 properties of parallelogram.
1. A diagonal of a parallelogram divides it into two congruent triangles.
2. Opposites sides of a parallelogram are congruent.
3. Opposite angles of a parallelogram are congruent.
4. Consecutive angles of a parallelogram are supplementary.
5. If one angle in a parallelogram is right, then all angles are right.
6. The diagonals of a parallelogram bisect each other.
Prove and apply properties of rectangles, rhombuses, and squares.
Use properties of rectangles, rhombuses, and squares to solve problems.
Prove that a given quadrilateral is a rectangle, rhombus, or square.
5.1 Introduction 5.2 Ratio And Proportionality 5.3 Similar Polygons 5.4 Basic Proportionality Theorem 5.5 Angle Bisector Theorem 5.6 Similar Triangles 5.7 Properties Of Similar Triangles
Macroeconomics- Movie Location
This will be used as part of your Personal Professional Portfolio once graded.
Objective:
Prepare a presentation or a paper using research, basic comparative analysis, data organization and application of economic information. You will make an informed assessment of an economic climate outside of the United States to accomplish an entertainment industry objective.
Biological screening of herbal drugs: Introduction and Need for
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Natural Products, In vitro evaluation techniques for Antioxidants, Antimicrobial and Anticancer drugs. In vivo evaluation techniques
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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.
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.
A Strategic Approach: GenAI in EducationPeter Windle
Artificial Intelligence (AI) technologies such as Generative AI, Image Generators and Large Language Models have had a dramatic impact on teaching, learning and assessment over the past 18 months. The most immediate threat AI posed was to Academic Integrity with Higher Education Institutes (HEIs) focusing their efforts on combating the use of GenAI in assessment. Guidelines were developed for staff and students, policies put in place too. Innovative educators have forged paths in the use of Generative AI for teaching, learning and assessments leading to pockets of transformation springing up across HEIs, often with little or no top-down guidance, support or direction.
This Gasta posits a strategic approach to integrating AI into HEIs to prepare staff, students and the curriculum for an evolving world and workplace. We will highlight the advantages of working with these technologies beyond the realm of teaching, learning and assessment by considering prompt engineering skills, industry impact, curriculum changes, and the need for staff upskilling. In contrast, not engaging strategically with Generative AI poses risks, including falling behind peers, missed opportunities and failing to ensure our graduates remain employable. The rapid evolution of AI technologies necessitates a proactive and strategic approach if we are to remain relevant.
Read| The latest issue of The Challenger is here! We are thrilled to announce that our school paper has qualified for the NATIONAL SCHOOLS PRESS CONFERENCE (NSPC) 2024. Thank you for your unwavering support and trust. Dive into the stories that made us stand out!
The French Revolution, which began in 1789, was a period of radical social and political upheaval in France. It marked the decline of absolute monarchies, the rise of secular and democratic republics, and the eventual rise of Napoleon Bonaparte. This revolutionary period is crucial in understanding the transition from feudalism to modernity in Europe.
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Artificial Intelligence (AI) technologies such as Generative AI, Image Generators and Large Language Models have had a dramatic impact on teaching, learning and assessment over the past 18 months. The most immediate threat AI posed was to Academic Integrity with Higher Education Institutes (HEIs) focusing their efforts on combating the use of GenAI in assessment. Guidelines were developed for staff and students, policies put in place too. Innovative educators have forged paths in the use of Generative AI for teaching, learning and assessments leading to pockets of transformation springing up across HEIs, often with little or no top-down guidance, support or direction.
This Gasta posits a strategic approach to integrating AI into HEIs to prepare staff, students and the curriculum for an evolving world and workplace. We will highlight the advantages of working with these technologies beyond the realm of teaching, learning and assessment by considering prompt engineering skills, industry impact, curriculum changes, and the need for staff upskilling. In contrast, not engaging strategically with Generative AI poses risks, including falling behind peers, missed opportunities and failing to ensure our graduates remain employable. The rapid evolution of AI technologies necessitates a proactive and strategic approach if we are to remain relevant.
Model Attribute Check Company Auto PropertyCeline George
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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.
1. Similar Figures and Proportions
Warm UpWarm Up
Problem of the DayProblem of the Day
Lesson PresentationLesson Presentation
2. Warm Up
Find the cross products, then tell whether the
ratios are equal.
Course 2
5-7 Similar Figures and Proportions
1.
16
6
, 40
15
2.
3
8
, 18
46
3.
8
9
, 24
27
4.
28
12
, 42
18
240 = 240; equal
216 = 216; equal
504 = 504; equal
138 = 144; not equal
3. Problem of the Day
Every 8th telephone pole along a road has a
red band painted on it. Every 14th pole has
an emergency call phone on it. What is the
number of the first pole with both a red
band and a call phone?
56
Course 2
5-7 Similar Figures and Proportions
4. Learn to use ratios to determine if two
figures are similar.
Course 2
5-7 Similar Figures and Proportions
6. Course 2
5-7 Similar Figures and Proportions
Octahedral fluorite is a crystal found in nature. It
grows in the shape of an octahedron, which is a
solid figure with eight triangular faces. The
triangles in different-sized fluorite crystals are
similar figures. Similar figures have the same
shape but not necessarily the same size.
7. Course 2
5-7 Similar Figures and Proportions
When naming similar figures, list the letters of the
corresponding vertices in the same order. In the
previous table ∆ABC ~ ∆DEF.
Writing Math
8. Course 2
5-7 Similar Figures and Proportions
Matching sides of two or more polygons
are called corresponding sides, and
matching angles are called
corresponding angles.
82◦
Corresponding
angles
D
E
F
Corresponding sides
A
B
C
82◦
55◦43◦ 55◦43◦
9. Course 2
5-7 Similar Figures and Proportions
SIMILAR FIGURES
Two figures are similar if
• The measures of their corresponding angles are
equal.
• The ratios of the lengths of the corresponding
sides are proportional.
10. Course 2
5-7 Similar Figures and Proportions
A side of a figure can be named by its endpoints,
with a bar above.
AB
Without the bar, the letters indicate the length of
the side.
Reading Math
11. Identify the corresponding sides in the pair of triangles.
Then use ratios to determine whether the triangles are
similar.
Additional Example 1: Determining Whether Two
Triangles Are Similar
Course 2
5-7 Similar Figures and Proportions
A C
B
10 in
4 in 7 in
D
E
F
16 in
28 in
40 in
AB corresponds to DE.
BC corresponds to EF.
AB
DE
=
? BC
EF
=
? AC
DF
4
16
7
28
10
40
1
4
1
4
1
4
Since the ratios of the corresponding sides are equivalent, the
triangles are similar.
Write ratios using the corresponding sides.
Substitute the length of the sides.
Simplify each ratio.
=
?
=
?
AC corresponds to DF.
=
?
=
?
12. Identify the corresponding sides in the pair of triangles.
Then use ratios to determine whether the triangles are
similar.
Check It Out: Example 1
Course 2
5-7 Similar Figures and Proportions
A C
B
9 in
3 in 7 in
D
E
F
9 in
21 in
27 in
AB corresponds to DE.
BC corresponds to EF.
AB
DE
=
? BC
EF
=
? AC
DF
3
9
7
21
9
27
1
3
1
3
1
3
Since the ratios of the corresponding sides are equivalent, the
triangles are similar.
Write ratios using the corresponding sides.
Substitute the length of the sides.
Simplify each ratio.
=
?
=
?
AC corresponds to DF.
=
?
=
?
13. Tell whether the figures are similar.
Additional Example 2: Determining Whether Two
Four-Sided Figures are Similar
Course 2
5-7 Similar Figures and Proportions
The corresponding angles of the
figures have equal measure.
Write each set of
corresponding sides as a ratio.
14. Additional Example 2 Continued
Course 2
5-7 Similar Figures and Proportions
MN
QR
MN corresponds to QR.
NO
RS
OP
ST
MP
QT
NO corresponds to RS.
OP corresponds to ST.
MP corresponds to QT.
15. Determine whether the ratios of the lengths of the
corresponding sides are proportional.
Additional Example 2 Continued
Course 2
5-7 Similar Figures and Proportions
Write ratios using
corresponding sides.
Substitute the length of
the sides.
Simplify each ratio.
Since the ratios of the corresponding sides are
equivalent, the figures are similar.
MN
QR
=
? NO
RS
=? OP
ST
=? MP
QT
6
9
=
? 8
12
=
? 4
6 =
? 10
15
2
3
= 2
3
= 2
3
= 2
3
? ? ?
16. Tell whether the figures are similar.
Check It Out: Example 2
Course 2
5-7 Similar Figures and Proportions
The corresponding angles of the
figures have equal measure.
100 m
80 m
60 m 47.5 m
80°
90°
125°
65°
M P
N
O
400 m
320 m
190 m240 m
80° 65°
90°
125°
Q T
R S
Write each set of
corresponding sides as a ratio.
17. Check It Out: Example 2 Continued
Course 2
5-7 Similar Figures and Proportions
MN
QR
MN corresponds to QR.
NO
RS
OP
ST
MP
QT
NO corresponds to RS.
OP corresponds to ST.
MP corresponds to QT.
100 m
80 m
60 m 47.5 m
80°
90°
125°
65°
M P
N
O
400 m
320 m
190 m240 m
80° 65°
90°
125°
Q T
R S
18. Determine whether the ratios of the lengths of the
corresponding sides are proportional.
Check It Out: Example 2 Continued
Course 2
5-7 Similar Figures and Proportions
Write ratios using corresponding
sides.
Substitute the length of the
sides.
Simplify each ratio.
Since the ratios of the corresponding sides
are equivalent, the figures are similar.
100 m
80 m
60 m 47.5 m
80°
90°
125°
65°
M P
N
O
400 m
320 m
190 m240 m
80° 65°
90°
125°
Q T
R S
MN
QR
=
? NO
RS
=
? OP
ST
=
? MP
QT
60
240 =
? 80
320 =
? 47.5
190 =
? 100
400
1
4
= 1
4
= 1
4
= 1
4
? ? ?
19. Lesson Quiz: Part I
Insert Lesson Title Here
Course 2
5-7 Similar Figures and Proportions
Tell whether the figures are similar.
1.
similar59°
59°
35°
35°
86°
86°
20. Lesson Quiz: Part II
Insert Lesson Title Here
Course 2
5-7 Similar Figures and Proportions
Tell whether the figures are similar.
2.
not similar
119°
55°
107°
79°
107°
80°
135°
38°