The document provides information about triangle congruence, including:
1. There are three postulates for proving triangles are congruent: side-side-side (SSS), side-angle-side (SAS), and angle-side-angle (ASA).
2. The SSS postulate states that if three sides of one triangle are congruent to three sides of a second triangle, then the triangles are congruent.
3. The SAS postulate states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of a second triangle, then the triangles are congruent.
4. The ASA postulate states that if two angles
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.
Determine what additional information is needed to prove two triangles congruent by a given theorem.
Create two-column proofs to show that two triangles are congruent.
This will help you in differentiating subsets of a line such as line segments, ray and opposite rays. Also in finding the number of line segments and rays in a given line.
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This learner's module talks about the topic Reasoning. It also includes the definition of Reasoning, Types of Reasoning (Inductive and Deductive Reasoning) and Examples of Reasoning for each type of reasoning.
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.
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.
Determine what additional information is needed to prove two triangles congruent by a given theorem.
Create two-column proofs to show that two triangles are congruent.
This will help you in differentiating subsets of a line such as line segments, ray and opposite rays. Also in finding the number of line segments and rays in a given line.
For more instructional resources, CLICK me here! 👇👇👇
https://tinyurl.com/y9muob6q
LIKE and FOLLOW me here! 👍👍👍
https://tinyurl.com/ycjp8r7u
https://tinyurl.com/ybo27k2u
This learner's module talks about the topic Reasoning. It also includes the definition of Reasoning, Types of Reasoning (Inductive and Deductive Reasoning) and Examples of Reasoning for each type of reasoning.
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.
Grade 9 (Alternate) Mathematics III - Learning Modules for EASE Program of DepEdR Borres
Grade 9 (Alternate) Mathematics III - Learning Modules for EASE Program of DepEd
A compilation of Math III learning modules for EASE which can be alternate for Grade 9 Mathematics.
Free!
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!
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Instructions for Submissions thorugh G- Classroom.pptxJheel Barad
This presentation provides a briefing on how to upload submissions and documents in Google Classroom. It was prepared as part of an orientation for new Sainik School in-service teacher trainees. As a training officer, my goal is to ensure that you are comfortable and proficient with this essential tool for managing assignments and fostering student engagement.
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:
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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.
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We all have good and bad thoughts from time to time and situation to situation. We are bombarded daily with spiraling thoughts(both negative and positive) creating all-consuming feel , making us difficult to manage with associated suffering. Good thoughts are like our Mob Signal (Positive thought) amidst noise(negative thought) in the atmosphere. Negative thoughts like noise outweigh positive thoughts. These thoughts often create unwanted confusion, trouble, stress and frustration in our mind as well as chaos in our physical world. Negative thoughts are also known as “distorted thinking”.
GIÁO ÁN DẠY THÊM (KẾ HOẠCH BÀI BUỔI 2) - TIẾNG ANH 8 GLOBAL SUCCESS (2 CỘT) N...
Math 8 – triangle congruence, postulates,
1. Pop Quiz: Identify
1. Two angles whose measures have a sum of 90deg
2. A statement that can be proven
3. Triangles in which corresponding parts (sides and angles) are equal in
measure
4. If a = b and b = c then a = c
5. a(b + c) = ab + ac
6. If a=b, then a+c=b+c
7. If a=b, then a-c=b-c
8. If a=b, then a/c=b/c
9. A point is an _________ term.
10. An angle is a __________ term
11. _________ are statements that are considered true without proof or validation.
2. Pop Quiz: Identify
1. Complementary Angles
2. Theorem
3. Congruent Triangles
4. Transitive Property of Equality
5. Distributive Property of Equality
6. Addition Property of Equality
7. Subtraction Property of Equality
8. Division Property of Equality
9. Undefined
10. Defined
11. Postulates
4. Objective
•At the end of this lesson, you should be
able to identify the conditions for which
two triangles are congruent.
5. Geometric figures are said to be congruent if
they have the same size and shape.
• Two triangles are congruent when all corresponding sides and
interior angles are congruent.
Consider Triangle QRS and IHG:
6. Triangles:
• The tick marks show that the corresponding sides are
congruent:
• 𝑄𝑅 ≅ 𝐼𝐻
• 𝑅𝑆 ≅ 𝐻𝐺
• 𝑆𝑄 ≅ 𝐺𝐼
• 𝑄𝑅 ≅ 𝐼𝐻
7. Triangles:
The angle arcs show that the corresponding
interior angles are congruent:
•∠Q≅∠I
•∠R≅∠H
•∠S≅∠G
•When all six statements are stated, then we can
conclude that △QRS≅△IHG.
9. Try it! Solution
•Since the two triangles are congruent,
then the corresponding sides are
congruent:
•AB≅DE
•BC≅EF
•AC≅DF
10. Try it! Solution
• Find x:
• x=AB, but from the congruence statement, AB=DE. This
means x=DE, too. From the figure, DE=14. Thus, x=14.
• Find y:
• y=FD, but from the congruence statement, FD=AC. This
means y=AC, too. From the figure, AC=12. Thus, y=12.
12. Objectives
• At the end of this lesson, you should be able to:
• enumerate the triangle congruence postulates;
• define the SSS, SAS, ASA postulates; and
• recognize congruent triangles using the triangle
congruence postulates.
13. There are three postulates for proving that
two triangles are congruent:
•Side-Side-Side (SSS) Congruence
Postulate
•Side-Angle-Side (SAS) Congruence
Postulate
•Angle-Side-Angle (ASA) Congruence
Postulate
14. SSS Congruence Postulate
• Postulate: The Side-Side-Side Congruence Postulate. If three
sides of one triangle are congruent to three sides of a second
triangle, then the two triangles are congruent.
15. SSS Congruence Postulate
• With reference to triangles ABC and XYZ:
• If 𝐴𝐵 ≅ 𝑋𝑌, 𝐵𝐶 ≅ 𝑌𝑍, and 𝐴𝐶 ≅ 𝑋𝑍, then △ABC≅△XYZ.
16. SAS Congruence Postulate
• Postulate: The Side-Angle-Side Congruence Postulate. If two sides
and the included angle of one triangle are congruent to two sides and
the included angle of a second triangle, then the two triangles are
congruent.
• Note: The included angle is any angle between two sides.
17. SAS Congruence Postulate
• With reference to triangles ABC and UVW:
• If 𝐴𝐶 ≅ 𝑈𝑊, ∠A≅∠U, and 𝐴𝐵 ≅ 𝑈𝑉, then △ABC≅△UVW.
18. ASA Congruence Postulate
• Postulate: The Angle-Side-Angle Congruence Postulate. If two angles
and the included side of one triangle are congruent to two angles and
the included side of a second triangle, then the two triangles are
congruent.
• Note: The included side is any side between two angles.
19.
20.
21.
22. Study the two congruent triangles in the
picture below. Which statement is true about
the second triangle?
23. • a) a = 7 cm, b = 8 cm, c = 9 cm
• b) a = 8 cm, b = 7 cm, c = 9 cm
• c) a = 8 cm, b = 9 cm, c = 7 cm
• d) a = 9 cm, b = 7 cm, c = 8 cm
24. Tip:
• You can determine which side/angle of one triangle corresponds
with which side/angle of another triangle by using the order of the
triangle names.
• Example: △ABC and △DEF.
• The first letters are A and D. This means ∠A is to ∠D. The second
letters are B and E, which means ∠B is to ∠E. The third set of
angles can be derived from the third letters.
• The name of sides uses two letters. The first two letters are AB and
DE, which means (𝐴𝐵 𝑖𝑠 𝑡𝑜 𝐷𝐸). The last two letters are BC and
EF (𝐵𝐶 𝑖𝑠 𝑡𝑜 𝐸𝐹), while the first and last letters are AC and
DF (𝐴𝐶 𝑖𝑠 𝑡𝑜 𝐷𝐹)respectively.
25. Keypoints
• There are three congruence postulates that can be used to tell if two
triangles are congruent:
• The Side-Side-Side (SSS) Congruence Postulate. If three sides of one
triangle are congruent to three sides of a second triangle, then the two
triangles are congruent.
• The Side-Angle-Side (SAS) Congruence Postulate. If two sides and the
included angle of one triangle are congruent to two sides and the included
angle of a second triangle, then the two triangles are congruent.
• The Angle-Side-Angle (ASA) Congruence Postulate. If two angles and
the included side of one triangle are congruent to two angles and the
included side of a second triangle, then the two triangles are congruent.