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McGraw Hill Integrated I, 2012
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McGraw Hill Integrated I, 2012 View details
6. Two-Dimensional Figures
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Exercise 1 Page 608

How can you check whether a polygon is convex?

Type of Polygon: Pentagon
Convex or Concave: Concave
Regular or Irregular: Irregular

Practice makes perfect

We are asked to name each polygon by its number of sides and then classify it as convex or concave, and regular or irregular. Let's start with the name.

Type of Polygon

Let's take a look at the given figure.

We can see that this polygon has five sides, so it is called a pentagon.

Convex or Concave

Next we can see that line BC has points in the interior of the polygon.

This means that the polygon is concave.

Regular or Irregular

Only convex polygons can be regular. Therefore, since our polygon is not convex, it must be irregular.

Extra

 When a Polygon Is Regular?

We already said that only convex polygons can be regular. However there are two more conditions that need to be satisfied in order to call a polygon regular.

  • Polygon must be equilateral — all sides must be congruent.
  • Polygon must be equiangular — all angles must be congruent.

As an example, every square is a regular polygon.

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arrow_right Check Your Understanding p.608
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arrow_right Practice and Problem Solving p.608-610
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arrow_right H.O.T. Problems p.610
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arrow_right Standardized Test Practice p.611
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arrow_right Spiral Review p.611
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arrow_right Skills Review p.611
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