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Математичне місто чотирикутників

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Математичне місто чотирикутників

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Розв'язати задачі:

Задача 1. Знайти кути паралелограма, якщо відомо, що один із них більший від другого на 50°.

Задача 2. Знайти довжини діагоналей прямокутника ABCD , якщо периметр його дорівнює 34 дм, а периметр одного із трикутників, на які діагональ АС поділила прямокутник, дорівнює 30 см.

Задача 3. Сторона ромба утворює з його діагоналями два кути, з яких один більший від другого на 50%. Обчислити кути ромба.

Кожна правильно розв'язана задача дає вам 6 балів, за три задачі одержуємо - 18 балів

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Difference Between Rhombus and Rectangle

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Learn about the properties of a rhombus and a rectangle and the difference between a rhombus and a rectangle with Cuemath.

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Розв'язок реальної задачі

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Розв'язок реальної задачі

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Охоронець має обійти територію підприємства по периметру. Відомо що швидкість руху охоронця дорівнює 4 км/год. Територія підприємства має форму прямокутника, у якого довжина більша від ширини на 200 м. Крім того, відомо, що сторони відносяться як 19:21. Скільки часу витратить охоронець на обхід?

Задача оцінюється в 10 балів

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Трапеції - Властивості

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Трапеції - Властивості

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Відео демонструє властивості трапеції, а також приклади задач і їх рішення.

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Чотирикутники в житті

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Чотирикутники в житті

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Учні досліджують, як чотирикутники використовуються в реальному житті, зокрема в архітектурі та інженерії.

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Real Life Applications of Quadrilaterals - GeeksforGeeks

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A Computer Science portal for geeks. It contains well written, well thought and well explained computer science and programming articles, quizzes and practice/competitive programming/company interview Questions.

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Підсумок та Тест

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Підсумок та Тест

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Резюме знань та онлайн тест для перевірки розуміння теми чотирикутників. Учні заповнюють тест як завершення вебквесту.

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Класифікація чотирикутників - Гра

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Класифікація чотирикутників - Гра

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Онлайн гра для учнів, де вони класифікують чотирикутники за їх характеристиками.

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In this interactive math activity, students will practice identifying quadrilaterals. This engaging math lesson gives students the opportunity to practice recognizing the various properties of quadrilaterals. A variety of question formats are presented to students in this educational, fun math game. One type of question asks students to drag the quadrilaterals with right angles into the box. Another question type states a word problem which students need to answer as "true" or "false." For example: "A rhombus has four equal sides and two pairs of parallel sides. True or false?" Yet another type of question presents a series of polygons in multiple choice format. The students must answer a question, such as, "Identify the quadrilateral that is a rectangle." There may be more than one answer, depending on the question.

This quadrilateral lesson gives students a limited amount of hints. The hints in this math lesson describe properties of a quadrilateral in detail. For example, "Hint: A rhombus has 4 equal sides and 2 pairs of parallel sides." The hints are intended to help students eliminate answers that don't fit the description or lead them to choose the answer that does match the quadrilateral described. After a student has used up all his or her hints in the math lesson, the hint window will display a message that says there are no more hints available.

You will be excited to know that a detailed explanation appears when a student chooses the wrong answer for any question in this interactive quadrilateral activity. The explanation page will include a description of the correct answer, including graphics of quadrilaterals, showing their angles and sides, as well as a detailed description of the properties of quadrilaterals. The explanations in this quadrilateral math lesson will help students learn from their mistakes as they move through the math lesson.

This geometry lesson hardly feels like math practice when students are immersed in the quadrilateral questions! Students think they are playing an entertaining and challenging math game, while teachers see the benefits of interactive math practice that they can use to monitor their students' progress in recognizing quadrilaterals. The interface is very kid-friendly and easy to use. The hint button in the lower-left corner of the screen is ready for students who need a nudge toward the right answer. A score-keeper in the upper-right corner of the screen tells students how many points they've earned. The progress icon above the score-keeper informs students how many questions they've completed in the quadrilateral activity.

The audio feature in this geometry math game allows students to listen to the question being read to them in a clear voice at the click of a button. This option is great for students who have difficulty reading, or for students with ESL/ELL needs.

We are eager for you and your students to try out this interactive quadrilateral game in your

Did you know you can try out I Know It lessons before you purchase a membership? You can preview this quadrilateral lesson, or any lesson, for free; however, the number of questions you can go through is limited until you become a member of the site.

Members are able to create student logins, view scores for completed lessons, adjust lesson settings, and access student progress reports.

I Know It also has amazing administrative tools for teachers. That's right! Teachers can create student logins, view their students' scores for completed lessons, adjust lesson settings, and access student progress reports.

As a bonus, teachers have the ability to assign lessons based on the individual needs and skill level of each student. This is possible because grade levels on I Know It are alternately referred to as "Level A," "Level B," "Level C," instead of "1st Grade," "2nd Grade," "3rd Grade," etc. Students won't know the lesson they're working on is associated with a specific grade level, making it easy for teachers to confirm that the math skills are suited to the child's ability.

We've categorized this quadrilaterals geometry activity as a Level D lesson. It may be appropriate to use at a third grade, fourth grade, or fifth grade level.

4.G.A.2
Geometry: Draw and Identify Lines and Angels, and Classify Shapes by Properties of Their Lines and Angles
Students should be able to classify two-dimensional shapes based on the presence or absence of perpendicular or parallel lines, or the presence or absence of angles of a specified size. Students should also be able to recognize right triangles and identify right angles.

Solid Shapes (Level D)
In this math activity, students will identify three-dimensional shapes. Cubes, cylinders, cones, spheres, and pyramids are covered in this math lesson. The terms faces and vertices are used.

Quadrilaterals (Level E)
In this math game, students will identify two-dimensional shapes. Right angles, parallel sides, parallelogram, square, rectangle, trapezoid are terms used in this geometry game.

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In this interactive math activity, students will practice identifying quadrilaterals. This engaging math lesson gives students the opportunity to practice recognizing the various properties of quadrilaterals. A variety of question formats are presented to students in this educational, fun math game. One type of question asks students to drag the quadrilaterals with right angles into the box.

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Вебквест присвячений в

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Вебквест присвячений вивченню чотирикутників - їхній

класифікації, властивостям та практичному застосуванню. Учні 8

класу маєте змогу закріпити та поглибити свої знання з

геометрії.

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День 1: Вступ до чотирикутників

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День 1: Вступ до чотирикутників

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Цей день присвячений ребусам. Кожна правильна відповідь 3 бали. Максимальна кількість балів - 18.

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e-GMAT Blog | Best GMAT blog on the planet

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In Euclidean geometry, a quadrilateral is a four-sided 2D figure whose sum of internal angles is 360°. The word quadrilateral is derived from two Latin words 'quadri' and 'latus' meaning four and side respectively. Therefore, identifying the properties of quadrilaterals is important when trying to distinguish them from other polygons.

So, what are the properties of quadrilaterals? There are two properties of quadrilaterals:

A quadrilateral should be closed shape with 4 sides

All the internal angles of a quadrilateral sum up to 360°

In this article, you will get an idea about the 5 types of quadrilaterals and get to know about the properties of quadrilaterals.

This is what you'll read in the article:

Here is a video explaining the properties of quadrilaterals:

The diagram given below shows a quadrilateral ABCD and the sum of its internal angles. All the internal angles sum up to 360°.

Thus, ∠A + ∠B + ∠C + ∠D = 360°

Different types of quadrilaterals

There are 5 types of quadrilaterals on the basis of their shape. These 5 quadrilaterals are:

Let's discuss each of these 5 quadrilaterals in detail:

Here are questions which will teach you how to apply the properties of all 5 quadrilaterals you'll learn in this article.

Rectangle

A rectangle is a quadrilateral with four right angles. Thus, all the angles in a rectangle are equal (360°/4 = 90°). Moreover, the opposite sides of a rectangle are parallel and equal, and diagonals bisect each other.

Properties of rectangles

A rectangle has three properties:

All the angles of a rectangle are 90°

Opposite sides of a rectangle are equal and Parallel

Diagonals of a rectangle bisect each other

Rectangle formula - Area and perimeter of a rectangle

If the length of the rectangle is L and breadth is B then,

1. Area of a rectangle = Length × Breadth or L × B

2. Perimeter of rectangle = 2 × (L + B)

These practice questions will help you solidify the properties of rectangles

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Square

Square is a quadrilateral with four equal sides and angles. It's also a regular quadrilateral as both its sides and angles are equal. Just like a rectangle, a square has four angles of 90° each. It can also be seen as a rectangle whose two adjacent sides are equal.

Properties of a square

For a quadrilateral to be a square, it has to have certain properties. Here are the three properties of squares:

All the angles of a square are 90°

All sides of a square are equal and parallel to each other

Diagonals bisect each other perpendicularly

Square formula - Area and perimeter of a square

If the side of a square is 'a' then,

1. Area of the square = a × a = a²

2. Perimeter of the square = 2 × (a + a) = 4a

These practice questions will help you solidify the properties of squares

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Parallelogram

A parallelogram, as the name suggests, is a simple quadrilateral whose opposite sides are parallel. Thus, it has two pairs of parallel sides. Moreover, the opposite angles in a parallelogram are equal and its diagonals bisect each other.

Properties of parallelogram

A quadrilateral satisfying the below-mentioned properties will be classified as a parallelogram. A parallelogram has four properties:

Opposite angles are equal

Opposite sides are equal and parallel

Diagonals bisect each other

Sum of any two adjacent angles is 180°

Parallelogram formulas - Area and perimeter of a parallelogram

If the length of a parallelogram is 'l', breadth is 'b' and height is 'h' then:

1. Perimeter of parallelogram= 2 × (l + b)

2. Area of the parallelogram = l × h

These practice questions will help you solidify the properties of parallelogram

Rhombus

A rhombus is a quadrilateral whose all four sides are equal in length and opposite sides are parallel to each other. However, the angles are not equal to 90°. A rhombus with right angles would become a square. Another name for rhombus is 'diamond' as it looks similar to the diamond suit in playing cards.

Properties of rhombus

A rhombus is a quadrilateral which has the following four properties:

Opposite angles are equal

All sides are equal and, opposite sides are parallel to each other

Diagonals bisect each other perpendicularly

Sum of any two adjacent angles is 180°

Rhombus formulas - Area and perimeter of a rhombus

If the side of a rhombus is a then, perimeter of a rhombus = 4a

If the length of two diagonals of the rhombus is d ₁ and d ₂ then the area of a rhombus = ½ × d ₁ × d ₂

These practice questions will help you solidify the properties of rhombus

Trapezium

A trapezium (called Trapezoid in the US) is a quadrilateral that has only one pair of parallel sides. The parallel sides are referred to as 'bases' and the other two sides are called 'legs' or lateral sides.

Properties of Trapezium

A trapezium is a quadrilateral in which the following one property:

Only one pair of opposite sides are parallel to each other

Trapezium formulas - Area and perimeter of a trapezium

If the height of a trapezium is ' h' (as shown in the above diagram) then:

1. Perimeter of the trapezium= Sum of lengths of all the sides = AB + BC + CD + DA

2. Area of the trapezium = ½ × (Sum of lengths of parallel sides) × h = ½ × (AB + CD) × h

These practice questions will help you solidify the properties of trapezium

Properties of quadrilaterals

The below table summarizes all the properties of the quadrilaterals that we have learned so far:

The below image also summarizes the properties of quadrilaterals:

Important quadrilateral formulas

The below table summarizes the formulas on the area and perimeter of different types of quadrilaterals:
Further reading:
Quadrilateral Practice Question

Let's practice the application of properties of quadrilaterals on the following sample questions:

GMAT Quadrilaterials Practice Question 1

Adam wants to build a fence around his rectangular garden of length 10 meters and width 15 meters. How many meters of fence he should buy to fence the entire garden?

Solution
Step 1: Given

Adam has a rectangular garden.

It has a length of 10 meters and a width of 15 meters.

He wants to build a fence around it.

Step 2: To find

The length required to build the fence around the entire garden.
Step 3: Approach and Working out
The fence can only be built around the outside sides of the garden.

So, the total length of the fence required= Sum of lengths of all the sides of the garden.

Since the garden is rectangular, the sum of the length of all the sides is nothing but the perimeter of the garden.

Perimeter = 2 × (10 + 15) = 50 metres

Hence, the required length of the fence is 50 meters.

Therefore, option E is the correct answer.

GMAT Quadrilaterials Practice Question 2

Steve wants to paint one rectangular-shaped wall of his room. The cost to paint the wall is $1.5 per square meter. If the wall is 25 meters long and 18 meters wide, then what is the total cost to paint the wall?

Solution
Step 1: Given

Steve wants to paint one wall of his room.

The wall is 25 meters long and 18 meters wide.

Cost to paint the wall is $1.5 per square meter.

Step 2: To find

The total cost to paint the wall.
Step 3: Approach and Working out

A wall is painted across its entire area.

So, if we find the total area of the wall in square meters and multiply it by the cost to paint 1 square meter of the wall then we can the total cost.

Area of the wall = length × Breadth = 25 metres × 18 metres = 450 square metre

Total cost to paint the wall = 450 × $1.5 = $675

Hence, the correct answer is option E.

We hope by now you would have learned the different types of quadrilaterals, their properties, and formulas and how to apply these concepts to solve questions on quadrilaterals. The application of quadrilaterals is important to solve geometry questions on the GMAT. If you are planning to take the GMAT, we can help you with high-quality study material which you can access for free by registering here.

Here are a few more articles on Math:

1. Improve accuracy in Math questions on Polygons

2. Geometry Questions - Most Common Mistakes | GMAT Quant Prep

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FAQs

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Properties of Quadrilaterals - rectangle, square, parallelogram, rhombus, trapezium

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In Euclidean geometry, a quadrilateral is a four-sided 2D figure whose sum of internal angles is 360°. The word quadrilateral is derived from two Latin words 'quadri' and 'latus' meaning four and side respectively. Therefore, identifying the properties of quadrilaterals is important when trying to distinguish them from other polygons.

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Паралелограми - Елементи

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Паралелограми - Елементи

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Учні досліджують елементи паралелограмів, використовуючи графіки та ілюстрації.

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Завдання: Виявити і сфотографувати чотирикутники в навколишньому середовищі (на вулиці, у класі або вдома). Скласти альбом чи колаж із фотографіями.

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Завдання: Виявити і сфотографувати чотирикутники в навколишньому середовищі (на вулиці, у класі або вдома). Скласти альбом чи колаж із фотографіями.

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Мета: Навчитися бачити застосування геометрії у повсякденому житті.

Інструменти: Фотоапарат або смартфон, інструменти для створення колажів.

Запитання для роздумів: Чому багато речей навколо нас мають форму чотирикутників? Які функції вони виконують?

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Інформація для роздумів

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Інформація для роздумів

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Архітектура

Використання чотирикутників у

проєктуванні будівель.

Інженерія

Застосування чотирикутників у

різних інженерних конструкціях.

Географія

Аналіз географічних об'єктів, що

мають форму чотирикутників.

Дизайн

Створення візерунків і

композицій із використанням

чотирикутників.

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За завдання третього дня ви отримуєте - 20 балів.

Тож загальна сума балів за три дні _ 56!

Це час міркувань. наполегливий час,

Й завдання давно вже чекають на вас.

Побажаю вам кмітливості,

За роботу, в добрий час!