Review the key concepts, formulae, and examples before starting your quiz.
🔑Concepts
Open Figures: These are figures that do not start and end at the same point. They have a gap or an 'opening' somewhere. Visualizing a piece of curved wire where the two ends are not touching helps identify an open figure, like the letter or .
Closed Figures: These are shapes that start and end at the exact same point, leaving no gaps. If you were to place a tiny ant inside a closed figure like a circle or a square, it could not get out without crossing over the boundary lines.
Simple Closed Figures: These are closed figures that do not cross or intersect themselves at any point. A circle or a triangle is a simple closed figure, whereas a figure-eight shape is not 'simple' because it crosses over itself at the center point.
Polygons: A polygon is a special type of closed figure that is made up entirely of straight line segments. For example, a triangle with straight sides is a polygon, but a circle is not a polygon because its boundary is a curved line.
Regions of a Closed Figure: Every closed figure has three distinct parts. The 'Interior' is the area inside the boundary, the 'Exterior' is the area outside the boundary, and the 'Boundary' is the line itself that forms the shape.
Line Segments in Figures: Figures are often made of line segments. In a closed polygon, the number of line segments determines its name. Visualizing a square, you can count equal line segments that meet at corners to close the shape.
Curves: Figures can be made of straight lines, curved lines, or both. A closed figure made only of curved lines is a circle or an oval. An open figure can also be a simple curve that looks like a snake moving across the ground.
📐Formulae
💡Examples
Problem 1:
Rahul draws a shape starting at point . He draws a straight line to point , then to point , and finally stops at point . Is this an open or a closed figure?
Solution:
Step 1: Identify the starting point, which is . \ Step 2: Identify the ending point, which is . \ Step 3: Compare the points. Since point is not the same as point (), there is an opening between them.
Explanation:
Because the figure does not return to its starting point, it is classified as an open figure.
Problem 2:
A polygon has vertices (corners) and all its sides are straight lines of equal length. If the figure is closed and simple, name the figure and identify how many line segments it has.
Solution:
Step 1: A closed figure with straight sides is called a quadrilateral. \ Step 2: Since all sides are of equal length and it is a simple closed figure, it is specifically a square. \ Step 3: Count the line segments: segments.
Explanation:
A square is a simple closed figure (polygon) made of equal line segments where the start and end points meet.