Study of quadrilaterals

Study of quadrilaterals

Quadrilateral by PhET Interactive Simulations, University of Colorado Boulder, licensed under CC-BY-4.0 (https://phet.colorado.edu)

Objective:

  • To know the definitions of rectangle, rhombus, and square and to generalize their properties and attributes.  

This virtual activity is designed to be used in math lessons in the next chapter:

  • Grade 8. “Polygons. Study of quadrilaterals”.

Theoretical Part

A quadrilateral is a special case of a polygon with four sides and four vertices.

Classification of quadrilaterals

  • Convex and concave: A convex quadrilateral is a quadrilateral in which any line connecting any two of its interior points lies completely inside the quadrilateral. A concave quadrilateral has concave angles, with at least one of the interior angles being a geometric figure greater than 180 degrees. 
  • Parallelogram: A quadrilateral whose opposite sides of a pair are parallel. 
  • Rectangle: a parallelogram whose angles are all right angles.
  • Square: a rectangle whose sides are all equal.
  • Rhombus: a parallelogram whose sides are all equal.
  • Trapezoid: a rectangle where only two opposite sides are parallel.

Properties of Rectangles

  • The sum of the interior angles of any rectangle is 360 degrees.
  • The diagonals of a rectangle are the segments that connect opposite vertices.
  • The centerlines of a rectangle are the segments connecting the centers of opposite sides.

Virtual experiment

In the “rectangles” simulation, students explore the properties and relationships between named square figures.

Workflow:

Step 1. In the work area you are provided with:

  • Rectangle (1);
  • A board with the name of the rectangle (2);
  • A button to restore the initial view of the rectangle (3);
  • Button to control music (4);
  • Buttons: marker, grid, diagonals, labels (5);
  • Small steps button (6);
  • Reset button (7).

Step 2. Activate the marker, grid, diagonals buttons. Marker, grid buttons help to compose the figure, diagonal button explore the diagonals of the figure.

Step 3. Build a rectangle from the given rectangle. To do this, you move the desired quantity by holding each of the points A, B, C, D. Check the correct figure by including a board with the name of the rectangle. The name is rectangle. Examine the diagonals of the figure.

Step 4. Construct a square. The name – square appears on the board. Study the diagonals of the shape.

Step 5. Press the Restore Initial View button each time to simplify the creation of each shape.

Step 6. Build a rhombus. The name on the board is Rhombus. Study the diagonals of the figure.

Step 7. Build a trapezoid with one 90-degree angle. The name on the board is trapezoid. Study the diagonals of the figure.

Step 8. Construct an isosceles trapezoid. The name isosceles trapezoid appears on the board. Examine the diagonals of the figure.

Step 9. Construct a parallelogram. The name on the board is parallelogram. Study the diagonals of the figure.

Step 10. Other compound rectangle types refer to convex rectangles. Try to construct convex rectangles of different shapes. The name on the board is convex quadrilateral.

Step 11. Construct a kind of rectangle in which at least one of the interior angles is greater than 180 degrees. This is a concave quadrilateral. The name on the board is concave quadrilateral. 

Conclusion

This virtual activity allows students to explore the types and diagonals of a rectangle. It is used as an aid to explore the similarities and differences of figures in geometry lessons.

Glossary of terms

  • Shape name hidden – Название фигуры скрыто – Фигураның атауы жасырылған
  • Reset shape – Сбросить фигуру – Пішінді қалпына келтіру
  • Marker – Маркер – Маркер
  • Grid – Сетка – Тор
  • Diagonals – Диагонали – Диагоналдар
  • Labels – Метки – Белгілер
  • Small steps – Маленькие шаги – Кішкентай қадамдар
  • Rectangle – Прямоугольник – Тіктөртбұрыш
  • Parallelogram – Параллелограмм – Параллелограмм
  • Square – Квадрат – Шаршы
  • Rhombus – Ромб – Ромб
  • Trapezoid – Трапеция -Трапеция
  • Isosceles trapezoid – Равнобедренная трапеция – Теңбүйірлі трапеция 
  • Convex quadrilateral – Выпуклый четырехугольник – Дөңес төртбұрыш
  • Concave quadrilateral – Вогнутый четырехугольник – Ойыс төртбұрыш