Euclidean geometry | Equivalence (mathematics)
In geometry, two figures or objects are congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the other. More formally, two sets of points are called congruent if, and only if, one can be transformed into the other by an isometry, i.e., a combination of rigid motions, namely a translation, a rotation, and a reflection. This means that either object can be repositioned and reflected (but not resized) so as to coincide precisely with the other object. So two distinct plane figures on a piece of paper are congruent if we can cut them out and then match them up completely. Turning the paper over is permitted. In elementary geometry the word congruent is often used as follows. The word equal is often used in place of congruent for these objects. * Two line segments are congruent if they have the same length. * Two angles are congruent if they have the same measure. * Two circles are congruent if they have the same diameter. In this sense, two plane figures are congruent implies that their corresponding characteristics are "congruent" or "equal" including not just their corresponding sides and angles, but also their corresponding diagonals, perimeters, and areas. The related concept of similarity applies if the objects have the same shape but do not necessarily have the same size. (Most definitions consider congruence to be a form of similarity, although a minority require that the objects have different sizes in order to qualify as similar.) (Wikipedia).
Introducing the Concept of Congruence
From playlist GeoGebra Geometry
In this video we continue discussing congruences and, in particular, we discuss solutions of linear congruences. The content of this video corresponds to Section 4.4 of my book "Number Theory and Geometry" which you can find here: https://alozano.clas.uconn.edu/number-theory-and-geometry/
From playlist Number Theory and Geometry
Triangle Congruence (quick review)
More resources available at www.misterwootube.com
From playlist Further Properties of Geometrical Figures
MIT 6.042J Mathematics for Computer Science, Spring 2015 View the complete course: http://ocw.mit.edu/6-042JS15 Instructor: Albert R. Meyer License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
From playlist MIT 6.042J Mathematics for Computer Science, Spring 2015
Number Theory | Congruence Modulo n -- Definition and Examples
We define the notion of congruence modulo n among the integers. http://www.michael-penn.net
From playlist Modular Arithmetic and Linear Congruences
Corresponding parts of congruent triangles are congruent
When two triangles are congruent, we can know that all of their corresponding sides and angles are congruent too!
From playlist High School Geometry | High School Math | Khan Academy
What is the Definition of Congruent Triangles - Congruent Triangles
👉 Learn about congruent triangles theorems. Two or more triangles (or polygons) are said to be congruent if they have the same shape and size. There are many methods to determine whether two triangles are congruent. Some of the methods include: (1) The SSS (Side Side Side) congruency the
From playlist Congruent Triangles
Number Theory - Basics of Congruences
From playlist â„•umber Theory
How to do a Geometry Proof – Step-by-Step Lesson
How to do a geometry proof. For more in-depth math help check out my catalog of courses. Every course includes over 275 videos of easy to follow and understand math instruction, with fully explained practice problems and printable worksheets, review notes and quizzes. All courses devel
From playlist Geometry
Update on Tropical Schemes by Diane Maclagan
PROGRAM COMBINATORIAL ALGEBRAIC GEOMETRY: TROPICAL AND REAL (HYBRID) ORGANIZERS Arvind Ayyer (IISc, India), Madhusudan Manjunath (IITB, India) and Pranav Pandit (ICTS-TIFR, India) DATE: 27 June 2022 to 08 July 2022 VENUE: Madhava Lecture Hall and Online Algebraic geometry is the study of
From playlist Combinatorial Algebraic Geometry: Tropical and Real (HYBRID)
Another congruence by transformation example | Congruence | Geometry | Khan Academy
Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/geometry/congruent-triangles/transformations-congruence/e/exploring-rigid-transformations-and-congruence?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry Watch the next lesson: https://www.kha
From playlist Mathematics I | High School Math | Khan Academy
Two column proof showing segments are perpendicular | Congruence | Geometry | Khan Academy
Using triangle congruency postulates to show that two intersecting segments are perpendicular Watch the next lesson: https://www.khanacademy.org/math/geometry/congruent-triangles/cong_triangle/v/finding-congruent-triangles?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry Missed the pr
From playlist High School Geometry | High School Math | Khan Academy
GEOMETRY Basics – Introduction to Common Notations and Symbols
https://tabletclass-academy.teachable.com/p/tabletclass-math-geometry1 TabletClass Math: https://tcmathacademy.com/ This video goes over geometry notation and symbols.
From playlist Geometry
Other triangle congruence postulates | Congruence | Geometry | Khan Academy
SSS, SAS, ASA and AAS postulates for congruent triangles. Showing AAA is only good for similarity and SSA is good for neither Watch the next lesson: https://www.khanacademy.org/math/geometry/congruent-triangles/cong_triangle/v/two-column-proof-showing-segments-are-perpendicular?utm_source
From playlist Mathematics I | High School Math | Khan Academy
Congruent triangles and SSS | Congruence | Geometry | Khan Academy
What it means for triangles to be congruent Watch the next lesson: https://www.khanacademy.org/math/geometry/congruent-triangles/cong_triangle/v/sss-to-show-a-radius-is-perpendicular-to-a-chord-that-it-bisects?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry Missed the previous lesson
From playlist Mathematics I | High School Math | Khan Academy
Congruent and Similar Triangles
working with similiar triangles, determining similar triangles http://mathispower4u.wordpress.com/
From playlist Geometry Basics
Example of rigid transformation and congruence | Congruence | Geometry | Khan Academy
Watch the next lesson: https://www.khanacademy.org/math/geometry/congruent-triangles/transformations-congruence/v/another-example-of-rigid-transformations-for-congruence?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry Missed the previous lesson? https://www.khanacademy.org/math/geome
From playlist Mathematics I | High School Math | Khan Academy
Another example of rigid transformations for congruence | Congruence | Geometry | Khan Academy
Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/geometry/congruent-triangles/transformations-congruence/e/defining-congruence-through-rigid-transformations?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry Watch the next lesson: https://www.
From playlist High School Geometry | High School Math | Khan Academy
Geometry Crash Course - Theorems for Congruent Triangles
Covers: - SSS - SAS - AAS - ASA - HL
From playlist Geometry Crash Course
Similarity postulates | Similarity | Geometry | Khan Academy
Thinking about what we need to know to determine whether two triangles are similar Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/geometry/similarity/triangle_similarlity/e/similar_triangles_1?utm_source=YT&utm_medium=Desc&utm_campaign=Geomet
From playlist High School Geometry | High School Math | Khan Academy