Introduction: Look around you! The surface of a blackboard, a kitchen table, and a notice board all lie on a flat surface called a plane.
Theory: In mathematics, figures drawn on flat surfaces using straight line segments and curved line segments are defined as plane figures.
Straight Line
Curved Line
Plane Figure (Flat)
NOT a Plane Figure (3D Ball)
Explanation: A plane figure must be on a completely flat surface. If a surface is curved, figures drawn on it do not count as plane figures. Lines used to draw these figures can be either straight or curved.
12.2 Closed Plane Figures and Open Figures
Introduction: Plane figures can either trap a space inside them completely or leave a gap open.
Theory: Plane figures which are completely bounded by line segments are defined as closed plane figures. Plane figures which are not completely bounded by line segments are called open figures.
Closed Figures (No way out!)
Open Figures (There's a gap!)
Explanation: Imagine the lines are fences. If the fence goes all the way around and meets at the start so nothing can get out, it is a closed figure. If there is a break or a gap in the fence, it is an open figure.
12.3 & 12.4 Rectilinear Plane Figures & Elements
Introduction: Now we will look at a very specific type of closed figure that is made up of only straight, rigid lines.
Theory: Closed figures bounded by straight line segments only are called closed rectilinear plane figures.
Elements: Side & Angle
NOT Rectilinear (It has a curve!)
Elements of the Figure:
Side: Any straight line segment of a rectilinear plane figure is defined as a side of the figure.
Angle: An angle formed inside a rectilinear plane figure by two sides meeting is defined as an angle of the plane figure.
12.5 Triangles and Quadrilaterals
Introduction: Let's organize rectilinear plane figures based on how many sides they have!
Theory:
Triangle: A closed rectilinear plane figure drawn with three straight line segments. It has three sides and three angles.
Quadrilateral: A closed rectilinear plane figure drawn with four straight line segments. It has four sides and four angles.
Properties of Quadrilaterals: In a quadrilateral, there are two pairs of sides which do not meet each other, defined as opposite sides.
Trapezium: The gap between one pair of opposite sides is constant.
Parallelogram: The gap between pairs of opposite sides is constant, and opposite sides are equal in length.
Rhombus: A parallelogram where all the sides are equal in length.
Rectangle: A parallelogram where all the angles are right angles.
Square: A rectangle with four equal sides.
Interactive Shape Explorer
Click on the buttons below to see each shape drawn on a grid and learn about its properties visually!
Square:
The gap between pairs of opposite sides is constant (parallel).