A polygon is a closed figure made of three or more straight line segments' A regular polygon is a po

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• A polygon is a closed figure made of three or
  more straight line segments. A regular polygon
  is a polygon whose sides and angles are equal.

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• We can identify polygons by observing their
  properties. Properties of polygons include sides
  (or edges) and angles (or corners). For example,
  we see that a rectangle has 2 pairs of parallel
  sides and 4 square angles, and that is how we
  know it is a rectangle. If we see a rectangle
  with 4 equal sides, we know it is a square.

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• Polygons are often named for the number and kinds
  of sides and angles they have. For example,
  triangles have 3 angles, quadrilaterals have 4
  sides, parallelograms are quadrilaterals with 2
  pairs of parallel sides, pentagons have 5 sides
  and 5 angles, hexagons have 6 sides and 6 angles,
  octagons have 8 sides and 8 angles, etc.

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• A line is a series of points that make a straight
  path on and on in either direction. When we talk
  about lines in geometry, we are talking about
  straight lines.
• A ray is a straight line that begins at a point
  and goes on and one in one direction.

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• A line segment is the part of a line between two
  points.
• A horizontal line is a line that runs left and
  right, like the horizon.

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• A vertical line is a line that runs up and down,
  like a telephone pole.
• Intersecting lines are tow lines that cross at
  only one point.
• Perpendicular lines are two lines that intersect
  or meet and make four square or right angles.
• Parallel lines are lines that never intersect and
  are always the same distance from each other at
  every point on the lines.

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• An angle is formed when two rays or line segments
  meet at a point called a vertex.
• A circle can be constructed around any point.
  Mathematicians agreed to divide a circle into
  360º. In other words, there are 360º around the
  midpoint, or center, of a circle.

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• Any angle is a portion of a circle. If it is not
  part of an actual circle, a circle can be
  constructed around the vertex of the angle, which
  would be the midpoint, or center.

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• To measure an angle, we place the vertex at the
  center of a circle and measure the number of
  degrees around the center of the circle between
  the two sides of the angle. That means that all
  angles measure 360º or less because angles are
  parts of a circle.
• A circle is a closed curved line equally distant
  from the center at every point on the lines.

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• A straight line makes a straight angle of 180º.
  In other words, there are 180º in the angle from
  one end point of the line around the center of
  the circle to the other end point of the line.
• Perpendicular lines make right, or square,
  angles, which measure 90º.
• Acute angles measure less than 90º and obtuse
  angles measure more than 90º.

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• Changing the lengths of the sides of an angle
  does not change the size of the angle.
• A protractor is a tool for measuring the number
  of degrees in an angle.

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• If you decide whether an angle is acute or obtuse
  before you measure it, then you will know which
  number scale on the protractor to use because an
  acute angle must be less than 90º and an obtuse
  angle must be more than 90º, so you use the scale
  that makes sense.

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• If angles are the same size, they are congruent
  angles. For example, all right angles are
  congruent.
• If line segments are the same length, they are
  congruent line segments. For example, all the
  sides of a square are congruent.

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• Congruent figures are figures that are the same
  size and shape. In other words, in congruent
  figures, the corresponding angles are congruent
  and the corresponding sides are congruent. For
  example, two four-inch squares are congruent.

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• Similar figures are figures that are the same
  shape, but might not be the same size. In other
  words, similar figures have congruent angles, but
  the sides might not be congruent. The
  corresponding sides are in the same ratio. For
  example, a four-inch square and a two-inch square
  are similar.

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• A pattern is an arrangement of things in some
  special order. For example, in jewelry-making
  the pattern for a necklace might be 3 large
  beads, 2 small beads, 3 large beads, etc.
• There are patterns all around us. There are
  patterns of shapes in buildings, clothing,
  jewelry, and art. Different patterns are used by
  different people and cultures around the world.

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• Every pattern has a rule that guides the order of
  the pattern. For example, the rule for the order
  of the days of the week is Sunday, Monday,
  Tuesday, Wednesday, Thursday, Friday, and
  Saturday.

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• When we change the position of a shape, we call
  that a transformation. A shape in a different
  position is not a different shape. The position
  of the object is transformed, not its shape.

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• There are three basic transformations slides
  (translations), turns (rotations), and flips
  (reflections).
• A slide, or translation, is when a shape is moved
  horizontally or vertically.

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• A turn, or rotation, is when an object is rotated
  either clockwise or counterclockwise.
• A flip, or reflection, is when an object is
  turned over to create a mirror image. Flips are
  often used to create symmetrical figures.

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• A figure is symmetrical if it can be folded,
  either mentally or physically, into two congruent
  halves positioned so that one half lies exactly
  on top of the other half. In other words, a
  figure is symmetrical if one half is a reflection
  of the other. A line of symmetry is a straight
  line lying exactly where a figure can be folded
  into two symmetrical halves.

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• Tessellations are one kind of pattern. When you
  cover an area with a pattern of polygons or other
  closed figures with no gaps and no overlapping,
  you have made a tessellation. For example, a
  tile floor or a brick wall are tessellations.

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• Coordinates are a pair of numbers that locate a
  point in relation to the axes. Coordinates are
  always written in the same order, so we call them
  ordered pairs. The first coordinate tells the
  sideways location and the second coordinate tells
  the up and down location.

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• Coordinates are a pair of numbers that locate a
  point in relation to the axes. Coordinates are
  always written in the same order, so we call them
  ordered pairs. The first coordinate tells the
  sideways location and the second coordinate tells
  the up and down location.

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• The distance around a shape or geometric figure
  is the perimeter.
• The length of the perimeter of any polygon is the
  sum of the lengths of all its sides. In other
  words, P the sum of the sides of a polygon.
• A pentomino is a shape made of five squares that
  each have at least one whole side in common with
  another square and no partial sides in common.

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• Area is the amount of space inside a flat
  (two-dimensional) shape.
• Area has two dimensions length and width. We
  measure area in square units of measure such as
  square inches or square centimeters because
  square units of measure indicate both length and
  width, not just length.

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• We find the area of a rectangle by multiplying
  the length by the width. The formula for finding
  the area of a rectangle is A 1 x w.

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• The formula for finding the area of a square is A
  s2.
• Figures with the same perimeters can have
  different areas. The closer the sides are to
  each other in length, the larger the area
  enclosed. For example, if a square and a
  rectangle have the same perimeter, the square
  will have a larger area.

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• We find the area of a square or rectangle by
  multiplying the length by the width. The formula
  for finding the area of a rectangle is A 1 x w.
• Area has two dimensions length and width. We
  measure area in square units of measure such as
  square inches or square centimeters because
  square units of measure indicate both length and
  width, not just length.

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• We find the area of a triangle by multiplying the
  height by the base and dividing that amount in
  half. The formula for the area of a triangle is
  A 1/2(b x h).

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• We estimate the area of irregular figures by
  counting the squares and partial squares inside
  the perimeter of the figure.
• When we estimate with fractions, we decide
  whether a fraction is near 0, 1/2, or 1. To
  estimate the area of an irregular shape, we need
  to look at each partial square and decide whether
  it is about 0 squares, about 1/2 square, or about
  1 square.

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• Plane figures have two dimensions, length and
  width. Solid figures take up space and have
  three dimensions length, width, and height.

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• Polyhedra and three-dimensional figures with
  curved surfaces are two kinds of solid figures.
  A solid figure with sides which are polygons is
  called a polyhedron. Polyhedra is the plural of
  polyhedron. Polyhedra include all kinds of
  prisms and pyramids. Solid figures with curved
  surfaces include spheres, cylinders, and cones.

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• Polyhedra have faces (sides), edges (lines where
  the sides join together), and vertices (vertex is
  the singular), or corners (points where edges
  meet). A cylinder has a curved surface and two
  circular or oval faces or bases. A cone has a
  curved surface, a circular or oval face or base,
  and a vertex. A sphere has only a curved surface.

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• A hexomino is a shape made of six squares that
  each have at least one whole side in common with
  another square and no partial sides in common.
• The surface area of a solid figure is the sum of
  the areas of all the faces or surfaces of the
  solid figure because these faces or surfaces
  cover the outside, or surface, of the figure.

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• The amount of space inside a solid figure is its
  volume. Volume has three dimensions - length,
  width, and height.
• Volume is measured in cubic units of measure
  because it has three dimensions - length, width,
  and height.

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• Volume is measured by finding the number of real
  or imaginary identical cubes that fit in a space.
  For example, if 24 centimeter cubes fit in a
  box, the volume of the box is 24 cubic
  centimeters.
• The volume of a rectangular prism is found by
  multiplying the length by the width by the
  height. The formula for finding the volume of a
  rectangular prism is V 1 x w x h.

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