Points, lines, and planes are the undefined terms in geometry that form its foundations. A point has no dimensions and marks a location in space, a line extends in one dimension, and a plane extends in two dimensions. The basic elements of 2D space are points, lines, line segments, rays, angles, and their intersections. Rays and angles are defined using points and lines, with rays having a starting point and angles consisting of two rays with the same starting point.
Fundamental Geometrical Concepts Class 7Tushar Gupta
I made this presentation for my school project after that I thought that I should upload it on any slide so I uploaded this to help others in making presentations and getting ideas.It is a class 7 project.
Fundamental Geometrical Concepts Class 7Tushar Gupta
I made this presentation for my school project after that I thought that I should upload it on any slide so I uploaded this to help others in making presentations and getting ideas.It is a class 7 project.
This is an interactive presentation which contains the information about Algebra for student-teacher , who are going to teach maths. Further, it contains information about the curriculum alignment and objectives of algebraic teaching which are mentioned in Curriculum of Pakistan.
Lesson plan on introduction of trigonometry, students must aware about the history , concepts to be done, what common error they commit and what are the scope of this topic in careers
If the two angles and an included side of one triangle are congruent to the corresponding two angles and an included side of another triangle, then the triangles are congruent.
By this end of the presentation you will be able to:
Identify and model points, lines, and planes.
Identify collinear and coplanar points.
Identify non collinear and non coplanar points.
This is an interactive presentation which contains the information about Algebra for student-teacher , who are going to teach maths. Further, it contains information about the curriculum alignment and objectives of algebraic teaching which are mentioned in Curriculum of Pakistan.
Lesson plan on introduction of trigonometry, students must aware about the history , concepts to be done, what common error they commit and what are the scope of this topic in careers
If the two angles and an included side of one triangle are congruent to the corresponding two angles and an included side of another triangle, then the triangles are congruent.
By this end of the presentation you will be able to:
Identify and model points, lines, and planes.
Identify collinear and coplanar points.
Identify non collinear and non coplanar points.
By this end of the presentation you will be able to:
Identify and model points, lines, and planes.
Identify collinear and coplanar points.
Identify non collinear and non coplanar points.
Acetabularia Information For Class 9 .docxvaibhavrinwa19
Acetabularia acetabulum is a single-celled green alga that in its vegetative state is morphologically differentiated into a basal rhizoid and an axially elongated stalk, which bears whorls of branching hairs. The single diploid nucleus resides in the rhizoid.
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!
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.
Synthetic Fiber Construction in lab .pptxPavel ( NSTU)
Synthetic fiber production is a fascinating and complex field that blends chemistry, engineering, and environmental science. By understanding these aspects, students can gain a comprehensive view of synthetic fiber production, its impact on society and the environment, and the potential for future innovations. Synthetic fibers play a crucial role in modern society, impacting various aspects of daily life, industry, and the environment. ynthetic fibers are integral to modern life, offering a range of benefits from cost-effectiveness and versatility to innovative applications and performance characteristics. While they pose environmental challenges, ongoing research and development aim to create more sustainable and eco-friendly alternatives. Understanding the importance of synthetic fibers helps in appreciating their role in the economy, industry, and daily life, while also emphasizing the need for sustainable practices and innovation.
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.
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
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.
How to Make a Field invisible in Odoo 17Celine George
It is possible to hide or invisible some fields in odoo. Commonly using “invisible” attribute in the field definition to invisible the fields. This slide will show how to make a field invisible in odoo 17.
Unit 8 - Information and Communication Technology (Paper I).pdfThiyagu K
This slides describes the basic concepts of ICT, basics of Email, Emerging Technology and Digital Initiatives in Education. This presentations aligns with the UGC Paper I syllabus.
2. Basics of Geometry
• What are the undefined terms in geometry?
• What concepts present the foundations of
geometry?
• What are the basic elements of 2D space?
3. Basics of Geometry
The terms points, lines, and planes are the foundations of
geometry, but…
point, line, and plane are all what we call undefined terms.
How can that be?
Well, any definition we could give them would depend on
the definition of some other mathematical idea that these
three terms help define. In other words, the definition would
be circular!
Undefined Terms?
4. Basics of Geometry
• Has no dimension
• Marks a location in space
• Usually represented by a small dot
Point
A
The above is called point A. Note the point
is represented with a capital letter.
5. Basics of Geometry
• Extend in one dimension.
• Represented with straight line with two arrowheads to
indicate that the line extends without end in two directions.
Line
l
B
A
This is Line l, (using the lower case
script letter) or symbolically we call it
NOTICE: The arrowheads are in
both directions on the symbol
6. Basics of Geometry
Plane
• Extend in two dimensions.
• Represented by a slanted 4 sided figure, but you
must envision it extends without end, even though
the representation has edges.
A
B C
M This is Plane M or plane ABC (be
sure to only use three
noncollinear points when naming
a plane)
7. Basics of Geometry
Collinear
• Collinear points are points that lie on the
same line.
l
C
A
B Points A, B and C are collinear.
8. Basics of Geometry
Coplanar
• Coplanar points are points that lie on the
same plane.
A
B
C Points A, B and C are coplanar.
9. Basics of Geometry
Line Segment
Let’s look at the idea of a point in between two other points on a line.
Here is line AB, or recall
symbolically
A B
The line segment does not
extend without end. It has
endpoints, in this case A and
B. The segment contains all
the points on the line
between A and B
A B
Notice the difference in the
symbolic notation!
This is segment
10. Basics of Geometry
Symbolized by
Ray
The initial point is
always the first
letter in naming a
ray. Notice the
difference in
symbols from both
a line and segment.
A B
A is called the initial
point
Ray AB extends in
one direction
without end.
Let’s look at a ray:
11. Basics of Geometry
Not all symbols are created equal!
Symbol alert!
is the same as
is the same as
BUT…
A B
A B
12. Basics of Geometry
is not the same as
Symbol alert!!
A B
A B
Initial point 1st
The ray is different!
Notice that the initial point is listed first in the symbol. Also note
that the symbolic ray always has the arrowhead on the right
regardless of the direction of the ray.
13. Basics of Geometry
If C is between A and B,
Opposite Rays
A BC
then and are opposite rays.
C is the common initial point for the rays!
14. Basics of Geometry
Angles
Rays are important because they help us define something very
important in geometry…Angles!
An angle consists of two different rays that have the same initial
point. The rays are sides of the angles. The initial point is called the
vertex.
vertex
sides
A
B
C
Notation: We denote an angle with
three points and symbol. The
middle point is always the vertex.
We can also name the angle with
just the vertex point. This angle can
be denoted as:
15. Basics of Geometry
Straight angle
m A = 180°
Obtuse angle
90°< m A < 180°
Acute angle
0°< m A < 90°
Classifying Angles
Angles are classified as acute, right, obtuse, and straight,
according to their measures. Angles have measures greater
than 0° and less or equal to 180°.
A A
Right angle
m A = 90°
A A
16. Basics of Geometry
Intersections of lines and planes
• Two or more geometric figures intersect if they have
one or more points in common.
• The intersection of the figures is the set of points the
figure has in common
Think!
!
How do 2 line intersect?
How do 2 planes intersect?
What about a line and a plane?
17. Basics of Geometry
Modeling Intersections
To think about the questions on the last slide lets look at the following…
B A
ETwo lines
intersect at a
point, like here
at point A. F
Line BF is the intersection of the
planes G and H.
G
H
Point E is the
intersection
of plane H
and line EC
D
C
18. Basics of Geometry
Something to think about…
You have just finished the first section in Geometry!
This is a very important section because it lays the foundation for
the rest of the year! Much of the vocabulary you will encounter in
this course will have its foundation in the ideas presented in this
lesson.
Can you name the three undefined terms in geometry? Do you
know the difference between and obtuse and straight angle? Can
you sketch the intersection of a plane and a line? How about two
planes? Can you visualize the intersection of two planes? How
about three?
The classfun and homefun provided will help you in developing a
better understanding of the concepts!
19. Basics of Geometry
Draw 3 noncollinear points J, K, L, then draw:
Quick Quiz!!!
L
K
J
When ready click to
see answers!
20. Basics of Geometry
Quick Quiz !!!!
1. Name 3 points that are collinear.
Points D, F and B lie on the same line, therefore they are collinear.
2. Name 4 points that are coplanar.
If you answered D, F, B, and G are coplanar, then you are correct. It
is harder to see because the plane is not drawn, but points D, F, B and
M are also coplanar.
3. Name 3 points that are not collinear.
There are many correct answers, D, F, M are
not coplanar.
M
G
D F
B
21. Basics of Geometry
Use the diagram below to answer the following questions.
a. Name the type of angle.
Acute
b. Name the vertex.
R
c. Name the sides of the angle.
d. Name the angle three different ways.
Quick Quiz !!!!
R
S
T