holt ca course 1 9-5 classifying polygons preparation for mg2.3 draw quadrilaterals and triangles...
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Holt CA Course 1
9-5 Classifying Polygons
Preparation for MG2.3 Draw quadrilaterals and triangles from given information about them (e.g., a quadrilateral having equal sides but no right angles, a right isosceles triangle).
California Standards
Holt CA Course 1
9-5 Classifying Polygons
Vocabulary
polygon
vertexregular polygon
Holt CA Course 1
9-5 Classifying PolygonsTriangles and rectangles are examples of polygons. A polygon is a closed plane figure formed by three or more line segments. Each line segment forms a side of the polygon. Each side meets exactly two other sides, one on each end, in a common endpoint. Each endpoint is a vertex of the polygon.
The polygon atleft has sixsides and sixvertices.
Vertices is plural for vertex.
Remember!
Side
Vertex
Holt CA Course 1
9-5 Classifying Polygons
Determine whether each figure is a polygon. Explain your answer.
Additional Example 1: Identifying Polygons
A. B.
The figure is a polygon. It is a closed figure with 4 line segments.
The figure is not a polygon. It is not a closed figure.
Holt CA Course 1
9-5 Classifying Polygons
Determine whether each figure is a polygon. Explain your answer.
Additional Example 1: Identifying Polygons
C. D.
The figure is not a polygon. The figure is not formed by line segments.
The figure is not a polygon. There are sides that meet more than 2 other sides.
Holt CA Course 1
9-5 Classifying Polygons
Determine whether each figure is a polygon. Explain your answer.
Check It Out! Example 1
A. B.
The figure is a polygon. It is a closed figure with 5 line segments.
The figure is not a polygon. It is not a closed figure.
Holt CA Course 1
9-5 Classifying Polygons
Determine whether each figure is a polygon. Explain your answer.
Check It Out! Example 1
C. D.
The figure is not a polygon. The figure is not formed by line segments.
The figure is not a polygon. There are sides that meet more than two other sides.
Holt CA Course 1
9-5 Classifying PolygonsPolygons are classified by the number of sidesand angles they have.
Triangle3 sides
3 angles
Quadrilateral4 sides
4 angles
Pentagon5 sides
5 angles
Hexagon6 sides
6 angles
Heptagon7 sides
7 angles
Octagon8 sides
8 angles
Nonagon9 sides
9 angles
Decagon10 sides
10 angles
Holt CA Course 1
9-5 Classifying Polygons
Name each polygon.
Additional Example 2: Classifying Polygons
A.
Octagon
B.
Quadrilateral
8 sides, 8 angles
4 sides, 4 angles
Holt CA Course 1
9-5 Classifying Polygons
Check It Out! Example 2
Name each polygon.
A. B.
Quadrilateral Pentagon
4 sides, 4 angles
5 sides, 5 angles
Holt CA Course 1
9-5 Classifying Polygons
A regular polygon is a polygon in which all sides are congruent and all angles are congruent.
Holt CA Course 1
9-5 Classifying PolygonsAdditional Example 3: Identifying and Classifying Regular
Polygons
Name each polygon and tell whether it is aregular polygon. Explain your answer.
The figure has congruent angles and congruent sides. It is a regular quadrilateral.
The figure is aquadrilateral. It is not a regular polygon becauseall of the sides are not congruent.
A. B.
Holt CA Course 1
9-5 Classifying Polygons
A polygon with congruent sides is not necessarily a regular polygon. Its angles must also be congruent.
Caution!
Holt CA Course 1
9-5 Classifying PolygonsCheck It Out! Example 3
The figure is a triangle. It is not a regular polygon because all sides and angles are not congruent.
The figure has congruent angles and congruent sides. It is a regular triangle.
Name each polygon and tell whether it is aregular polygon. If it is not, explain why not.
A. B.