The document discusses proving triangle congruence using the ASA and AAS postulates. It provides examples showing how to use these postulates to prove triangles are congruent. Specifically, it gives step-by-step workings through two examples proving triangle congruence using ASA and AAS. It also includes an example problem solving for a missing side length in a right triangle where the hypotenuse and one leg are given.
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
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.
Ethnobotany and Ethnopharmacology:
Ethnobotany in herbal drug evaluation,
Impact of Ethnobotany in traditional medicine,
New development in herbals,
Bio-prospecting tools for drug discovery,
Role of Ethnopharmacology in drug evaluation,
Reverse Pharmacology.
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.
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.
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.
Palestine last event orientationfvgnh .pptxRaedMohamed3
An EFL lesson about the current events in Palestine. It is intended to be for intermediate students who wish to increase their listening skills through a short lesson in power point.
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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
This is a presentation by Dada Robert in a Your Skill Boost masterclass organised by the Excellence Foundation for South Sudan (EFSS) on Saturday, the 25th and Sunday, the 26th of May 2024.
He discussed the concept of quality improvement, emphasizing its applicability to various aspects of life, including personal, project, and program improvements. He defined quality as doing the right thing at the right time in the right way to achieve the best possible results and discussed the concept of the "gap" between what we know and what we do, and how this gap represents the areas we need to improve. He explained the scientific approach to quality improvement, which involves systematic performance analysis, testing and learning, and implementing change ideas. He also highlighted the importance of client focus and a team approach to quality improvement.
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. ESSENTIAL QUESTIONS
How do you use the ASA Postulate to test for triangle
congruence?
How do you use the AAS Postulate to test for triangle
congruence?
4. VOCABULARY
1. Included Side: The side between two consecutive
angles in a triangle
Postulate 4.3 - Angle-Side-Angle (ASA) Congruence:
Theorem 4.5 - Angle-Angle-Side (AAS) Congruence:
5. VOCABULARY
1. Included Side: The side between two consecutive
angles in a triangle
Postulate 4.3 - Angle-Side-Angle (ASA) Congruence: If
two angles and the included side of one triangle are
congruent to two angles and included side of a
second triangle, then the triangles are congruent
Theorem 4.5 - Angle-Angle-Side (AAS) Congruence:
6. VOCABULARY
1. Included Side: The side between two consecutive
angles in a triangle
Postulate 4.3 - Angle-Side-Angle (ASA) Congruence: If
two angles and the included side of one triangle are
congruent to two angles and included side of a
second triangle, then the triangles are congruent
Theorem 4.5 - Angle-Angle-Side (AAS) Congruence: If
two angles and the nonincluded side of one triangle
are congruent to the corresponding angles and
nonincluded side of a second triangle, then the
triangles are congruent
7. EXAMPLE 1
Prove the following.
Prove: △WRL ≅△EDL
Given: L is the midpoint of WE,WR ! ED
8. EXAMPLE 1
Prove the following.
Prove: △WRL ≅△EDL
Given: L is the midpoint of WE,WR ! ED
1. L is the midpoint of WE,WR ! ED
9. EXAMPLE 1
Prove the following.
Prove: △WRL ≅△EDL
1. Given
Given: L is the midpoint of WE,WR ! ED
1. L is the midpoint of WE,WR ! ED
10. EXAMPLE 1
Prove the following.
Prove: △WRL ≅△EDL
1. Given
Given: L is the midpoint of WE,WR ! ED
2. WL ≅ EL
1. L is the midpoint of WE,WR ! ED
11. EXAMPLE 1
Prove the following.
Prove: △WRL ≅△EDL
1. Given
Given: L is the midpoint of WE,WR ! ED
2. WL ≅ EL 2. Midpoint Thm.
1. L is the midpoint of WE,WR ! ED
12. EXAMPLE 1
Prove the following.
Prove: △WRL ≅△EDL
1. Given
Given: L is the midpoint of WE,WR ! ED
2. WL ≅ EL 2. Midpoint Thm.
3. ∠WLR ≅ ∠ELD
1. L is the midpoint of WE,WR ! ED
13. EXAMPLE 1
Prove the following.
Prove: △WRL ≅△EDL
1. Given
Given: L is the midpoint of WE,WR ! ED
2. WL ≅ EL 2. Midpoint Thm.
3. ∠WLR ≅ ∠ELD 3. Vertical Angles Thm.
1. L is the midpoint of WE,WR ! ED
14. EXAMPLE 1
Prove the following.
Prove: △WRL ≅△EDL
1. Given
Given: L is the midpoint of WE,WR ! ED
2. WL ≅ EL 2. Midpoint Thm.
3. ∠WLR ≅ ∠ELD 3. Vertical Angles Thm.
4. ∠LWR ≅ ∠LED
1. L is the midpoint of WE,WR ! ED
15. EXAMPLE 1
Prove the following.
Prove: △WRL ≅△EDL
1. Given
Given: L is the midpoint of WE,WR ! ED
2. WL ≅ EL 2. Midpoint Thm.
3. ∠WLR ≅ ∠ELD 3. Vertical Angles Thm.
4. ∠LWR ≅ ∠LED 4. Alternate Interior Angles Thm
1. L is the midpoint of WE,WR ! ED
16. EXAMPLE 1
Prove the following.
Prove: △WRL ≅△EDL
1. Given
Given: L is the midpoint of WE,WR ! ED
2. WL ≅ EL 2. Midpoint Thm.
3. ∠WLR ≅ ∠ELD 3. Vertical Angles Thm.
4. ∠LWR ≅ ∠LED 4. Alternate Interior Angles Thm
5. △WRL ≅△EDL
1. L is the midpoint of WE,WR ! ED
17. EXAMPLE 1
Prove the following.
Prove: △WRL ≅△EDL
1. Given
Given: L is the midpoint of WE,WR ! ED
2. WL ≅ EL 2. Midpoint Thm.
3. ∠WLR ≅ ∠ELD 3. Vertical Angles Thm.
4. ∠LWR ≅ ∠LED 4. Alternate Interior Angles Thm
5. △WRL ≅△EDL 5. ASA
1. L is the midpoint of WE,WR ! ED
19. EXAMPLE 2
Prove the following.
Prove: LN ≅ MN
Given: ∠NKL ≅ ∠NJM, KL ≅ JM
1. ∠NKL ≅ ∠NJM, KL ≅ JM
20. EXAMPLE 2
Prove the following.
Prove: LN ≅ MN
Given: ∠NKL ≅ ∠NJM, KL ≅ JM
1. ∠NKL ≅ ∠NJM, KL ≅ JM 1. Given
21. EXAMPLE 2
Prove the following.
Prove: LN ≅ MN
Given: ∠NKL ≅ ∠NJM, KL ≅ JM
1. ∠NKL ≅ ∠NJM, KL ≅ JM 1. Given
2. ∠N ≅ ∠N
22. EXAMPLE 2
Prove the following.
Prove: LN ≅ MN
Given: ∠NKL ≅ ∠NJM, KL ≅ JM
1. ∠NKL ≅ ∠NJM, KL ≅ JM 1. Given
2. ∠N ≅ ∠N 2. Reflexive
23. EXAMPLE 2
Prove the following.
Prove: LN ≅ MN
Given: ∠NKL ≅ ∠NJM, KL ≅ JM
1. ∠NKL ≅ ∠NJM, KL ≅ JM 1. Given
2. ∠N ≅ ∠N 2. Reflexive
3. △JNM ≅△KNL
24. EXAMPLE 2
Prove the following.
Prove: LN ≅ MN
Given: ∠NKL ≅ ∠NJM, KL ≅ JM
1. ∠NKL ≅ ∠NJM, KL ≅ JM 1. Given
2. ∠N ≅ ∠N 2. Reflexive
3. △JNM ≅△KNL 3. AAS
25. EXAMPLE 2
Prove the following.
Prove: LN ≅ MN
Given: ∠NKL ≅ ∠NJM, KL ≅ JM
1. ∠NKL ≅ ∠NJM, KL ≅ JM 1. Given
2. ∠N ≅ ∠N 2. Reflexive
3. △JNM ≅△KNL 3. AAS
4. LN ≅ MN
26. EXAMPLE 2
Prove the following.
Prove: LN ≅ MN
Given: ∠NKL ≅ ∠NJM, KL ≅ JM
1. ∠NKL ≅ ∠NJM, KL ≅ JM 1. Given
2. ∠N ≅ ∠N 2. Reflexive
3. △JNM ≅△KNL 3. AAS
4. LN ≅ MN 4. Corresponding Parts
of Congruent Triangles
are Congruent (CPCTC)
27. EXAMPLE 3
On a template design for a certain envelope, the top
and bottom flaps are isosceles triangles with congruent
bases and base angles. If EV = 8 cm and the height of
the isosceles triangle is 3 cm, find PO.
28. EXAMPLE 3
On a template design for a certain envelope, the top
and bottom flaps are isosceles triangles with congruent
bases and base angles. If EV = 8 cm and the height of
the isosceles triangle is 3 cm, find PO.
EV ≅ PL, so each segment has a measure
of 8 cm. If an auxiliary line is drawn
from point O perpendicular to PL, you
will have a right triangle formed.
29. EXAMPLE 3
On a template design for a certain envelope, the top
and bottom flaps are isosceles triangles with congruent
bases and base angles. If EV = 8 cm and the height of
the isosceles triangle is 3 cm, find PO.
EV ≅ PL, so each segment has a measure
of 8 cm. If an auxiliary line is drawn
from point O perpendicular to PL, you
will have a right triangle formed.
In the right triangle, we have one leg (the height) of 3 cm.
The auxiliary line will bisect PL, as point O is equidistant
from P and L.
