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

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• A polygon is a closed figure made of three or
  more straight line segments (sides). A regular
  polygon is a polygon that has equal sides and
  equal angles.

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• We can identify different polygons by looking for
  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 angels 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,
  and octagons have 8 sides and 8 angles, etc.

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• Triangles can be classified by the size of their
  angles. Obtuse triangles have one obtuse angle -
  one angle larger than 90º. Acute triangles have
  all three acute angles - all three angles smaller
  than 90º. Right triangles have one right angle -
  one 90º angle.

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• Triangles can be classified by the sides.
  Equilateral triangles have all three sides equal.
  Isosceles triangles have two equal sides.
  Scalene triangles have no equal sides.

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• Triangles are the most basic polygons. All other
  polygons can be divided into triangles.

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• Mathematicians have agreed to divide a circle
  into 360º. In other words, there are 360º around
  the midpoint, or center, of a circle. Any angle
  is a portion of a circle. If an angle is not
  part of an actual circle, a circle could be
  constructed around it with the vertex of the
  angles as 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.

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• The sum of the angles of any triangle is 180º.
• Sides of a polygon are name by their end points,
  which are the vertices of the polygon. For
  example, the side between vertex A and vertex B
  is called side AB.

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• Angles can be named three ways. An angle can be
  named by its vertex. For example, the vertex of
  ?A is at point A. An angle can be named by its
  sides two ways. For example, if the sides of ?A
  are side AB and side AC, then the angle would be
  named ?BAC or ?CAB. The vertex must always be
  the middle letter in the angle name.

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• A protractor is a tool for measuring the number
  of degrees in an angle.
• Before you measure an angle, decide whether it is
  acute or obtuse. Remember, an acute angle is
  less than 90º. Use the scale on the protractor
  that makes sense for the size of that angle.

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• Changing the lengths of the sides of an angle
  does not change the size of the angle.

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• Changing the lengths of the sides of an angle
  does not change the size of the angle.
• Sides of a polygon are named by their end points,
  which are their vertices of the polygon. For
  example, the side between vertex W and vertex X
  is called side WX.

Gr5-U5-L4
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• Angles can be named three ways. An angle can be
  named by its vertex. For example, the vertex of
  ?W is at point W. An angle can be named by its
  sides two ways. For example, if the sides of ?W
  are side WZ and side WX, then the angle would be
  named ?XWZ or ?ZWX. The vertex must always be
  the middle letter in the angle name.

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• A compass is a tool for constructing circles, or
  arcs which are parts of circles.

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• A circle has a center, circumference, radius, and
  diameter. The circumference is the distance
  around the circle. The radius of a circle is a
  straight line from the center to any point on the
  circumference. The diameter of a circle is a
  straight line from one point on the circumference
  through the center of the circle to another point
  on the circumference.

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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 six-inch squares are congruent.

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• Similar figures are figures that are the same
  shape, but are not necessarily 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 ration.
  For example, a right triangle with sides of 1
  in., 2 in., and 21/4 in. is similar to a right
  triangle with corresponding sides of 2 in., 4
  in., and 41/2 in.

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• All circles are similar because they are the same
  shape and have 360º around their centers. Only
  circles with the same radius or diameter are
  congruent.

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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.
• A turn, or rotation, is when an object is rotated
  either clockwise or counterclockwise.

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• 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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• For a figure to be symmetrical, it needs two
  properties
• 1. Both halves need to be
• congruent.
• 2. The halves need to be
• positioned so that they are
• reflections of each other.

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• Tessellations are a 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.

Gr5-U5-L8
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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 polygon or other
  two-dimensional shape 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 sum of the sides.

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• The distance around a circle is called the
  circumference.
• Pi is a number that mathematicians use to find
  the circumference and area of circles. Pi is
  represented by the symbol (?). Pi (?) equals
  about 3.14.
• The circumference of a circle equals pi (?) times
  the diameter
• C ?d.

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• 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 length and
  width, not just length.

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• 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 the larger area.

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• We find the area of a trapezoid by dividing it
  into a rectangle and one or two triangles,
  finding the areas of the component parts, and
  then adding to find the total area.
• 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.

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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 finding 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 that 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 face or base, and a vertex. A
  sphere has only a curved surface.

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• A pyramid has triangular faces and any polygon as
  a base. A prism has square or rectangular faces
  and a pair of any congruent polygons as bases.
  Each prism and pyramid is classified by the shape
  of its base or bases.

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• 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. Since volume has three
  dimensions, it is measured in cubic units of
  measure.

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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 four 1-centimeter cubes make a
  rectangular prism is 4 cubic centimeters.

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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 sixteen 1-centimeter cubes fit
  in a box, the volume of the box is 16 cubic
  centimeters.

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• 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.
• Since the volume has three dimensions (length,
  width, and height), it is measured in cubic units
  of measure.

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