1. The document discusses properties and congruence of triangles. It defines congruence as two triangles being the same shape and size with corresponding angles and sides equal.
2. There are five criteria for congruence: side-angle-side, angle-side-angle, angle-angle-side, side-side-side, and right angle-hypotenuse-side.
3. Additional properties discussed include isosceles triangles having equal angles opposite equal sides, and relationships between sides and opposite angles/angles and opposite sides in all triangles.
A plane figure with three sides and three angles is called a triangle. We will learn the different types of triangles based on varying side lengths and angle measurements. After this session you can very easily tell the difference between all types of triangles and know the mathematics involved in it.
Did you know, two different triangles of different sizes can be similar to each other based on the ratio of their sides ?
Here you will learn the following:
1) Criteria’s for similarity
2) Scale factor
3) Congruency
If the corresponding sides of a triangle is twice than that of another triangle, will the area be also doubled??
Watch this session to learn about the effects that can be seen in areas of two similar triangles in just 10 minutes.
Basic Proportionality Theorem is one of the important topics of a Triangle that deals with the study of the proportion of the two sides of a triangle. So, watch this session and learn about the Theorem and its proof.
Pythagoras theorem is a fundamental relation in Euclidean geometry among the three sides of a right triangle.
In this session, you will learn this very important theorem and learn to prove its statement with its proof in a geometric way.
A plane figure with three sides and three angles is called a triangle. We will learn the different types of triangles based on varying side lengths and angle measurements. After this session you can very easily tell the difference between all types of triangles and know the mathematics involved in it.
Did you know, two different triangles of different sizes can be similar to each other based on the ratio of their sides ?
Here you will learn the following:
1) Criteria’s for similarity
2) Scale factor
3) Congruency
If the corresponding sides of a triangle is twice than that of another triangle, will the area be also doubled??
Watch this session to learn about the effects that can be seen in areas of two similar triangles in just 10 minutes.
Basic Proportionality Theorem is one of the important topics of a Triangle that deals with the study of the proportion of the two sides of a triangle. So, watch this session and learn about the Theorem and its proof.
Pythagoras theorem is a fundamental relation in Euclidean geometry among the three sides of a right triangle.
In this session, you will learn this very important theorem and learn to prove its statement with its proof in a geometric way.
Areas related to Circles - class 10 maths Amit Choube
This a ppt which is based on chapter circles of class 10 maths it is a very good ppt which will definitely enhance your knowledge . it will also clear all concepts and doubts about this chapter and its topics
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
PROJECT (PPT) ON PAIR OF LINEAR EQUATIONS IN TWO VARIABLES - CLASS 10mayank78610
THIS A PROJECT BEING MADE BY INFORMATION COLLECTED FROM CLASS 10 MATHS NCERT BOOK.
THANK YOU FOR SEEING MY PROJECT ... I THINK THIS MIGHT HELP YOU IN YOUR HOLIDAY HOMEWORK PROJECTS .
Trigonometry Presentation For Class 10 StudentsAbhishek Yadav
Presentation on Trigonometry. A topic for class 10 Students. Has every topic covered for students wanting to make a presentation on Trigonometry. Hope this will help you...........
Areas related to Circles - class 10 maths Amit Choube
This a ppt which is based on chapter circles of class 10 maths it is a very good ppt which will definitely enhance your knowledge . it will also clear all concepts and doubts about this chapter and its topics
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
PROJECT (PPT) ON PAIR OF LINEAR EQUATIONS IN TWO VARIABLES - CLASS 10mayank78610
THIS A PROJECT BEING MADE BY INFORMATION COLLECTED FROM CLASS 10 MATHS NCERT BOOK.
THANK YOU FOR SEEING MY PROJECT ... I THINK THIS MIGHT HELP YOU IN YOUR HOLIDAY HOMEWORK PROJECTS .
Trigonometry Presentation For Class 10 StudentsAbhishek Yadav
Presentation on Trigonometry. A topic for class 10 Students. Has every topic covered for students wanting to make a presentation on Trigonometry. Hope this will help you...........
Techniques to optimize the pagerank algorithm usually fall in two categories. One is to try reducing the work per iteration, and the other is to try reducing the number of iterations. These goals are often at odds with one another. Skipping computation on vertices which have already converged has the potential to save iteration time. Skipping in-identical vertices, with the same in-links, helps reduce duplicate computations and thus could help reduce iteration time. Road networks often have chains which can be short-circuited before pagerank computation to improve performance. Final ranks of chain nodes can be easily calculated. This could reduce both the iteration time, and the number of iterations. If a graph has no dangling nodes, pagerank of each strongly connected component can be computed in topological order. This could help reduce the iteration time, no. of iterations, and also enable multi-iteration concurrency in pagerank computation. The combination of all of the above methods is the STICD algorithm. [sticd] For dynamic graphs, unchanged components whose ranks are unaffected can be skipped altogether.
Chatty Kathy - UNC Bootcamp Final Project Presentation - Final Version - 5.23...John Andrews
SlideShare Description for "Chatty Kathy - UNC Bootcamp Final Project Presentation"
Title: Chatty Kathy: Enhancing Physical Activity Among Older Adults
Description:
Discover how Chatty Kathy, an innovative project developed at the UNC Bootcamp, aims to tackle the challenge of low physical activity among older adults. Our AI-driven solution uses peer interaction to boost and sustain exercise levels, significantly improving health outcomes. This presentation covers our problem statement, the rationale behind Chatty Kathy, synthetic data and persona creation, model performance metrics, a visual demonstration of the project, and potential future developments. Join us for an insightful Q&A session to explore the potential of this groundbreaking project.
Project Team: Jay Requarth, Jana Avery, John Andrews, Dr. Dick Davis II, Nee Buntoum, Nam Yeongjin & Mat Nicholas
As Europe's leading economic powerhouse and the fourth-largest hashtag#economy globally, Germany stands at the forefront of innovation and industrial might. Renowned for its precision engineering and high-tech sectors, Germany's economic structure is heavily supported by a robust service industry, accounting for approximately 68% of its GDP. This economic clout and strategic geopolitical stance position Germany as a focal point in the global cyber threat landscape.
In the face of escalating global tensions, particularly those emanating from geopolitical disputes with nations like hashtag#Russia and hashtag#China, hashtag#Germany has witnessed a significant uptick in targeted cyber operations. Our analysis indicates a marked increase in hashtag#cyberattack sophistication aimed at critical infrastructure and key industrial sectors. These attacks range from ransomware campaigns to hashtag#AdvancedPersistentThreats (hashtag#APTs), threatening national security and business integrity.
🔑 Key findings include:
🔍 Increased frequency and complexity of cyber threats.
🔍 Escalation of state-sponsored and criminally motivated cyber operations.
🔍 Active dark web exchanges of malicious tools and tactics.
Our comprehensive report delves into these challenges, using a blend of open-source and proprietary data collection techniques. By monitoring activity on critical networks and analyzing attack patterns, our team provides a detailed overview of the threats facing German entities.
This report aims to equip stakeholders across public and private sectors with the knowledge to enhance their defensive strategies, reduce exposure to cyber risks, and reinforce Germany's resilience against cyber threats.
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Empowering the Data Analytics Ecosystem: A Laser Focus on Value
The data analytics ecosystem thrives when every component functions at its peak, unlocking the true potential of data. Here's a laser focus on key areas for an empowered ecosystem:
1. Democratize Access, Not Data:
Granular Access Controls: Provide users with self-service tools tailored to their specific needs, preventing data overload and misuse.
Data Catalogs: Implement robust data catalogs for easy discovery and understanding of available data sources.
2. Foster Collaboration with Clear Roles:
Data Mesh Architecture: Break down data silos by creating a distributed data ownership model with clear ownership and responsibilities.
Collaborative Workspaces: Utilize interactive platforms where data scientists, analysts, and domain experts can work seamlessly together.
3. Leverage Advanced Analytics Strategically:
AI-powered Automation: Automate repetitive tasks like data cleaning and feature engineering, freeing up data talent for higher-level analysis.
Right-Tool Selection: Strategically choose the most effective advanced analytics techniques (e.g., AI, ML) based on specific business problems.
4. Prioritize Data Quality with Automation:
Automated Data Validation: Implement automated data quality checks to identify and rectify errors at the source, minimizing downstream issues.
Data Lineage Tracking: Track the flow of data throughout the ecosystem, ensuring transparency and facilitating root cause analysis for errors.
5. Cultivate a Data-Driven Mindset:
Metrics-Driven Performance Management: Align KPIs and performance metrics with data-driven insights to ensure actionable decision making.
Data Storytelling Workshops: Equip stakeholders with the skills to translate complex data findings into compelling narratives that drive action.
Benefits of a Precise Ecosystem:
Sharpened Focus: Precise access and clear roles ensure everyone works with the most relevant data, maximizing efficiency.
Actionable Insights: Strategic analytics and automated quality checks lead to more reliable and actionable data insights.
Continuous Improvement: Data-driven performance management fosters a culture of learning and continuous improvement.
Sustainable Growth: Empowered by data, organizations can make informed decisions to drive sustainable growth and innovation.
By focusing on these precise actions, organizations can create an empowered data analytics ecosystem that delivers real value by driving data-driven decisions and maximizing the return on their data investment.
Adjusting primitives for graph : SHORT REPORT / NOTESSubhajit Sahu
Graph algorithms, like PageRank Compressed Sparse Row (CSR) is an adjacency-list based graph representation that is
Multiply with different modes (map)
1. Performance of sequential execution based vs OpenMP based vector multiply.
2. Comparing various launch configs for CUDA based vector multiply.
Sum with different storage types (reduce)
1. Performance of vector element sum using float vs bfloat16 as the storage type.
Sum with different modes (reduce)
1. Performance of sequential execution based vs OpenMP based vector element sum.
2. Performance of memcpy vs in-place based CUDA based vector element sum.
3. Comparing various launch configs for CUDA based vector element sum (memcpy).
4. Comparing various launch configs for CUDA based vector element sum (in-place).
Sum with in-place strategies of CUDA mode (reduce)
1. Comparing various launch configs for CUDA based vector element sum (in-place).
Levelwise PageRank with Loop-Based Dead End Handling Strategy : SHORT REPORT ...Subhajit Sahu
Abstract — Levelwise PageRank is an alternative method of PageRank computation which decomposes the input graph into a directed acyclic block-graph of strongly connected components, and processes them in topological order, one level at a time. This enables calculation for ranks in a distributed fashion without per-iteration communication, unlike the standard method where all vertices are processed in each iteration. It however comes with a precondition of the absence of dead ends in the input graph. Here, the native non-distributed performance of Levelwise PageRank was compared against Monolithic PageRank on a CPU as well as a GPU. To ensure a fair comparison, Monolithic PageRank was also performed on a graph where vertices were split by components. Results indicate that Levelwise PageRank is about as fast as Monolithic PageRank on the CPU, but quite a bit slower on the GPU. Slowdown on the GPU is likely caused by a large submission of small workloads, and expected to be non-issue when the computation is performed on massive graphs.
2. We know that a closed figure formed by three intersecting
lines is called a triangle(‘Tri’ means ‘three’).A triangle has
three sides, three angles and three vertices. For e.g.-in
Triangle ABC, denoted as ∆ABC AB,BC,CA are the three
sides, ∠A,∠B,∠C are three angles and A,B,C are three
vertices.
A
B C
3. OBJECTIVES IN THIS LESSON
1
• INEQUALITIES IN A TRIANGLE.
2
• STATE THE CRITERIA FOR THE CONGRUENCE OF TWO
TRIANGLES.
3
• SOME PROPERTIES OF A TRIANGLE.
4
•DEFINE THE CONGRUENCE OF TRIANGLE.
4. DEFINING THE CONGRUENCE OF TRIANGLE:-
Let us take ∆ABC and ∆XYZ such that
corresponding angles are equal and
corresponding sides are equal :-
A
B C
X
Y Z
CORRESPONDING PARTS
∠A=∠X
∠B=∠Y
∠C=∠Z
AB=XY
BC=YZ
AC=XZ
5. Now we see that sides of ∆ABC coincides with sides of
∆XYZ.
A
B C
X
Y Z
SO WE GET THAT
TWO TRIANGLES ARE CONGRUENT, IF ALL THE
SIDES AND ALL THE ANGLES OF ONE TRIANGLE
ARE EQUAL TO THE CORRESPONDING SIDES AND
ANGLES OF THE OTHER TRIANGLE.
Here, ∆ABC ≅ ∆XYZ
6. This also means that:-
A corresponds to X
B corresponds to Y
C corresponds to Z
For any two congruent triangles the corresponding
parts are equal and are termed as:-
CPCT – Corresponding Parts of Congruent Triangles
7. CRITERIAS FOR CONGRUENCE OF TWO TRIANGLES
SAS(side-angle-side) congruence
• Two triangles are congruent if two sides and the included angle of one triangle are
equal to the two sides and the included angle of other triangle.
ASA(angle-side-angle) congruence
• Two triangles are congruent if two angles and the included side of one triangle are
equal to two angles and the included side of other triangle.
AAS(angle-angle-side) congruence
• Two triangles are congruent if any two pairs of angle and one pair of corresponding
sides are equal.
SSS(side-side-side) congruence
• If three sides of one triangle are equal to the three sides of another triangle, then the
two triangles are congruent.
RHS(right angle-hypotenuse-side) congruence
• If in two right-angled triangles the hypotenuse and one side of one triangle are equal to
the hypotenuse and one side of the other triangle, then the two triangles are congruent.
8. A
B C
P
Q R
S(1) AC = PQ
A(2) ∠C = ∠R
S(3) BC = QR
Now If,
Then ∆ABC ≅ ∆PQR (by SAS congruence)
9. A
B C
D
E F
Now If, A(1) ∠BAC = ∠EDF
S(2) AC = DF
A(3) ∠ACB = ∠DFE
Then ∆ABC ≅ ∆DEF (by ASA congruence)
10. A
B C P
Q
R
Now If, A(1) ∠BAC = ∠QPR
A(2) ∠CBA = ∠RQP
S(3) BC = QR
Then ∆ABC ≅ ∆PQR (by AAS congruence)
11. Now If, S(1) AB = PQ
S(2) BC = QR
S(3) CA = RP
A
B C
P
Q R
Then ∆ABC ≅ ∆PQR (by SSS congruence)
12. Now If, R(1) ∠ABC = ∠DEF = 90°
H(2) AC = DF
S(3) BC = EF
A
B C
D
E F
Then ∆ABC ≅ ∆DEF (by RHS congruence)
13. PROPERTIES OF TRIANGLE
A
B C
A Triangle in which two sides are equal in length is called
ISOSCELES TRIANGLE. So, ∆ABC is a isosceles triangle with
AB = BC.
14. Angles opposite to equal sides of an isosceles triangle are equal.
B C
A
Here, ∠ABC = ∠ ACB
15. The sides opposite to equal angles of a triangle are equal.
CB
A
Here, AB = AC
16. Theorem on inequalities in a triangle
If two sides of a triangle are unequal, the angle opposite to the longer side is
larger ( or greater)
10
8
9
Here, by comparing we will get that-
Angle opposite to the longer side(10) is greater(i.e. 90°)
17. In any triangle, the side opposite to the longer angle is longer.
10
8
9
Here, by comparing we will get that-
Side(i.e. 10) opposite to longer angle (90°) is longer.
18. The sum of any two side of a triangle is greater than the third
side.
10
8
9
Here by comparing we get-
9+8>10
8+10>9
10+9>8
So, sum of any two sides is greater than the third side.
19. SUMMARY
1.Two figures are congruent, if they are of the same shape and size.
2.If two sides and the included angle of one triangle is equal to the two sides and
the included angle then the two triangles are congruent(by SAS).
3.If two angles and the included side of one triangle are equal to the two angles
and the included side of other triangle then the two triangles are congruent( by
ASA).
4.If two angles and the one side of one triangle is equal to the two angles and the
corresponding side of other triangle then the two triangles are congruent(by AAS).
5.If three sides of a triangle is equal to the three sides of other triangle then the
two triangles are congruent(by SSS).
6.If in two right-angled triangle, hypotenuse one side of the triangle are equal to
the hypotenuse and one side of the other triangle then the two triangle are
congruent.(by RHS)
7.Angles opposite to equal sides of a triangle are equal.
8.Sides opposite to equal angles of a triangle are equal.
9.Each angle of equilateral triangle are 60°
10.In a triangle, angles opposite to the longer side is larger
11.In a triangle, side opposite to the larger angle is longer.
12.Sum of any two sides of triangle is greater than the third side.