The document discusses proportion and similar triangles in geometry. It defines proportion as an equation stating that two ratios are equal, and provides examples of using cross products to check for proportion. It then defines similar polygons and triangles as those with congruent corresponding angles and proportional corresponding sides. The document provides different methods to prove triangles are similar, including SAS, SSS, and AA similarity. It also discusses how corresponding parts of similar triangles, such as perimeters, altitudes, angle bisectors, and medians are proportional. Several theorems and examples involving parallel lines cutting across triangles proportionally are presented.
Maths (CLASS 10) Chapter Triangles PPT
thales theorem
similar triangles
phyathagoras theorem ,etc
In this ppt all theorem are proved solution are gven
there are videos also
all topic cover
Maths (CLASS 10) Chapter Triangles PPT
thales theorem
similar triangles
phyathagoras theorem ,etc
In this ppt all theorem are proved solution are gven
there are videos also
all topic cover
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.
June 3, 2024 Anti-Semitism Letter Sent to MIT President Kornbluth and MIT Cor...Levi Shapiro
Letter from the Congress of the United States regarding Anti-Semitism sent June 3rd to MIT President Sally Kornbluth, MIT Corp Chair, Mark Gorenberg
Dear Dr. Kornbluth and Mr. Gorenberg,
The US House of Representatives is deeply concerned by ongoing and pervasive acts of antisemitic
harassment and intimidation at the Massachusetts Institute of Technology (MIT). Failing to act decisively to ensure a safe learning environment for all students would be a grave dereliction of your responsibilities as President of MIT and Chair of the MIT Corporation.
This Congress will not stand idly by and allow an environment hostile to Jewish students to persist. The House believes that your institution is in violation of Title VI of the Civil Rights Act, and the inability or
unwillingness to rectify this violation through action requires accountability.
Postsecondary education is a unique opportunity for students to learn and have their ideas and beliefs challenged. However, universities receiving hundreds of millions of federal funds annually have denied
students that opportunity and have been hijacked to become venues for the promotion of terrorism, antisemitic harassment and intimidation, unlawful encampments, and in some cases, assaults and riots.
The House of Representatives will not countenance the use of federal funds to indoctrinate students into hateful, antisemitic, anti-American supporters of terrorism. Investigations into campus antisemitism by the Committee on Education and the Workforce and the Committee on Ways and Means have been expanded into a Congress-wide probe across all relevant jurisdictions to address this national crisis. The undersigned Committees will conduct oversight into the use of federal funds at MIT and its learning environment under authorities granted to each Committee.
• The Committee on Education and the Workforce has been investigating your institution since December 7, 2023. The Committee has broad jurisdiction over postsecondary education, including its compliance with Title VI of the Civil Rights Act, campus safety concerns over disruptions to the learning environment, and the awarding of federal student aid under the Higher Education Act.
• The Committee on Oversight and Accountability is investigating the sources of funding and other support flowing to groups espousing pro-Hamas propaganda and engaged in antisemitic harassment and intimidation of students. The Committee on Oversight and Accountability is the principal oversight committee of the US House of Representatives and has broad authority to investigate “any matter” at “any time” under House Rule X.
• The Committee on Ways and Means has been investigating several universities since November 15, 2023, when the Committee held a hearing entitled From Ivory Towers to Dark Corners: Investigating the Nexus Between Antisemitism, Tax-Exempt Universities, and Terror Financing. The Committee followed the hearing with letters to those institutions on January 10, 202
Welcome to TechSoup New Member Orientation and Q&A (May 2024).pdfTechSoup
In this webinar you will learn how your organization can access TechSoup's wide variety of product discount and donation programs. From hardware to software, we'll give you a tour of the tools available to help your nonprofit with productivity, collaboration, financial management, donor tracking, security, and more.
Honest Reviews of Tim Han LMA Course Program.pptxtimhan337
Personal development courses are widely available today, with each one promising life-changing outcomes. Tim Han’s Life Mastery Achievers (LMA) Course has drawn a lot of interest. In addition to offering my frank assessment of Success Insider’s LMA Course, this piece examines the course’s effects via a variety of Tim Han LMA course reviews and Success Insider comments.
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.
For more information, visit-www.vavaclasses.com
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!
Model Attribute Check Company Auto PropertyCeline George
In Odoo, the multi-company feature allows you to manage multiple companies within a single Odoo database instance. Each company can have its own configurations while still sharing common resources such as products, customers, and suppliers.
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.
Biological screening of herbal drugs: Introduction and Need for
Phyto-Pharmacological Screening, New Strategies for evaluating
Natural Products, In vitro evaluation techniques for Antioxidants, Antimicrobial and Anticancer drugs. In vivo evaluation techniques
for Anti-inflammatory, Antiulcer, Anticancer, Wound healing, Antidiabetic, Hepatoprotective, Cardio protective, Diuretics and
Antifertility, Toxicity studies as per OECD guidelines
2. Proportion
• An equation stating that
two ratios are equal
– Example:
• Cross products: means
and extremes
– Example:
d
c
b
a
d
c
b
a
a and d = extremes
b and c = means
ad = bc
3. Similar Polygons
• Similar polygons have:
• Congruent corresponding angles
• Proportional corresponding sides
• Scale factor: the ratio of corresponding sides
A
B
C D
E
L
M
N O
P
Polygon ABCDE ~ Polygon LMNOP
NO
CD
LM
AB
Ex:
4. Similar Triangles
• Similar triangles have
congruent
corresponding angles
and proportional
corresponding sides
A
B
C
Y
X
Z
ABC ~ XYZ
angle A angle X
angle B angle Y
angle C angle Z
YZ
BC
XZ
AC
XY
AB
5. Similar Triangles
• Triangles are similar if you show:
– Any 2 pairs of corresponding sides are
proportional and the included angles are
congruent (SAS Similarity)
A
B
C
R
S
T
18
12 6
4
6. Similar Triangles
• Triangles are similar if you show:
– All 3 pairs of corresponding sides are
proportional (SSS Similarity)
A
B
C
R
S
T
10
14
6
7
5
3
7. Similar Triangles
• Triangles are similar if you show:
– Any 2 pairs of corresponding angles are
congruent (AA Similarity)
A
B
C
R
S
T
8. Parts of Similar Triangles
• If two triangles are
similar, then the
perimeters are
proportional to the
measures of
corresponding sides
XZ
AC
YZ
BC
XY
AB
XYZ
perimeter
ABC
perimeter
A
B C
X
Y Z
9. Parts of Similar Triangles
• the measures of the
corresponding altitudes
are proportional to the
corresponding sides
• the measures of the
corresponding angle
bisectors are
proportional to the
corresponding sides
YZ
BC
YX
BA
XZ
AC
XW
AD
A
B C
X
Y Z
D
W
L
M
N
O
R
S
T
U
RT
LN
RS
LM
ST
MN
SU
MO
If two triangles are similar:
10. Parts of Similar Triangles
• If 2 triangles are similar,
then the measures of the
corresponding medians
are proportional to the
corresponding sides.
• An angle bisector in a triangle
cuts the opposite side into
segments that are proportional
to the other sides
G
H I
J
T
U V W
UW
HJ
TW
GJ
UT
GH
TV
GI
A
B
C
D
E
F
G
H
AD
AB
CD
BC
EH
EF
GH
FG
11. Theorem
Triangle Proportionality Theorem
If a line is parallel to one side of a
triangle and intersects the other two
sides, then it divides the two sides
proportionally.
EC
AE
DB
AD
12. Converse of the Triangle
Proportionally Theorem
If a line divides two sides of a triangle
proportionally, then the line is parallel
to the remaining side.
BC
DE
EC
AE
DB
AD
//
13. Parallel Lines and Proportional
Parts
• Triangle Midsegment
Theorem
– A midsegment of a
triangle is parallel to
one side of a triangle,
and its length is half of
the side that it is
parallel to
A
B
C
D
E
*If E and B are the midpoints
of AD and AC respectively,
then EB = DC
2
1
14. Theorem
If three parallel lines are intersected by
two lines, then the lines are divided
proportionally.
15. Parallel Lines and Proportional
Parts
• If 3 or more lines are
parallel and intersect
two transversals, then
they cut the
transversals into
proportional parts
EF
DE
BC
AB
A
B
C
D
E
F
EF
BC
DF
AC
EF
DF
BC
AC
16. Parallel Lines and Proportional
Parts
• If 3 or more parallel
lines cut off congruent
segments on one
transversal, then they
cut off congruent
segments on every
transversal
BC
AB
A
B
C
D
E
F
EF
DE
If , then
17. Theorem
If a ray bisects one angle of a triangle,
then it divides the sides proportional
with the sides they are touching.
28. A. Determine whether the triangles are similar. If so, write a
similarity statement. Explain your reasoning.
29. B. Determine whether the triangles are similar. If so, write a
similarity statement. Explain your reasoning.
30. A. Determine whether the triangles
are similar. If so, write a similarity
statement. Explain your reasoning.
31. B. Determine whether the triangles are
similar. If so, write a similarity
statement. Explain your reasoning.
32. A. Determine whether the triangles are
similar. If so, choose the correct similarity
statement to match the given data.
33. B. Determine whether the triangles are
similar. If so, choose the correct
similarity statement to match the given
data.
34. ALGEBRA Given , RS = 4, RQ = x + 3,
QT = 2x + 10, UT = 10, find RQ and QT.
35. SKYSCRAPERS Josh wanted to measure the height of the Sears
Tower in Chicago. He used a
12-foot light pole and measured its shadow at 1 p.m. The length
of the shadow was 2 feet. Then he measured the length of the
Sears Tower’s shadow and it
was 242 feet at the same time.
What is the height of the
Sears Tower?