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Learn it your way
A short class with Sarah and her students. The other ways are under More.
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Today we're diving into the world of polygons. Can anyone tell me what a polygon is?
Isn't it a shape that has straight lines?
Exactly! A polygon is a simple closed curve made up entirely of line segments. Let’s remember this by using the acronym 'SIMPLE' — it’s a 'Shape with Interconnected Multiple Line Edges.'
What about those shapes that bulge inwards? Are they still polygons?
Great question! Those types are called concave polygons. Meanwhile, shapes like triangles or squares that don’t bulge are convex polygons. Let's draw some examples on the board!
How can we identify a convex shape?
A good way to remember is that all interior angles in a convex shape are less than 180 degrees. So, when in doubt, check the angles!
What about regular polygons?
Regular polygons are both equilateral and equiangular. Remember this with the phrase 'Equal Angles, Equal Sides' or 'EASE'. They have uniform lengths and angles, like a square.
Can you all summarize what we've learned?
We learned about polygons, and that there are convex and concave types.
Exactly! Keep those concepts in mind as we move forward.
Now let's explore the differences between regular and irregular polygons. Who can tell me what makes a polygon regular?
It has to have equal sides and angles.
That's right! And what can we say about irregular polygons?
They don't have equal sides or angles!
Correct! To remember, think of the word 'IRREGULAR' — it signifies 'Inconsistent Ratios of Edges and Angles.' Let's draw a few examples and label them now.
Why are some polygons only classified as regular?
Regular polygons are more symmetrical and easier to work with mathematically. They help us in defining further geometric concepts. Let's summarize: Regular polygons are equiangular and equilateral, while irregular ones are not.
So, can all quadrilaterals be regular?
No, not all quadrilaterals can be regular. For example, a rectangle is equiangular but not equilateral. Remember, polygons need to satisfy both conditions to be regular.
Well done! Keep practicing these classifications in your notes.
Now let's put our knowledge to the test! I want each of you to draw one convex and one concave polygon. Label them as well.
Can my concave shape have a point that's inward?
Yes! An inward point defines a concave shape. Great observation!
I drew a quadrilateral that looks like a 'U' shape. Is that concave?
Exactly! Any lines drawn inside that 'U' touch the outside. How about your convex shape, Student_1?
I drew a square! All angles are less than 180 degrees.
Perfect! It's all about identifying those interior angles. Finally, can we quickly recap what makes a polygon regular?
It has equal sides and angles!
Great work today! Keep practicing these concepts at home.
Polygons are shapes, with edges straight and true; Convex is all inward—concave's a curve or two.
Once upon a time in Polygon Land, the convex shapes danced happily, with no inward bends. However, in the corner of the land, the concave shapes formed a shape with a dramatic dip in the middle. They all knew their places!
Use 'CELEBRATE' to recall: C for Concave, E for Edges inward, L for Less than 180 degrees, E for Equal angles in Regular, B for Both angles in Rectangle (not regular), R for Regular descriptions, A for All angles in square (not in concave).
Remember 'P-C-R-I' for Polygons, Convex, Regular, Irregular.
Term
Polygon
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Term
Regular Polygon
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Term
Concave Polygon
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Term
Convex Polygon
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A simple closed curve made up of line segments.
A polygon where all interior angles are less than 180 degrees.
A polygon with at least one interior angle greater than 180 degrees.
A polygon that is equiangular and equilateral.
A polygon that is neither equiangular nor equilateral.
This section introduces the basic concepts of polygons, differentiating between convex and concave shapes, as well as regular and irregular polygons.
In this section, we explore the definition of polygons and classify them into convex and concave categories. We also discuss regular polygons, defined by equal side lengths and angles, and irregular polygons. Understanding these classifications is fundamental to studying more complex geometrical shapes later in the chapter.
This section lays the foundational concepts for understanding quadrilaterals by first explaining what polygons are. A polygon is defined as a simple closed curve formed by joining a number of points with line segments without retracing any part. The section categorizes polygons into two main types:
This primer on polygons provides essential knowledge and terminology that sets the stage for more complex discussions about quadrilaterals later in this chapter.