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Geometric Sense
Lesson 13
Symmetry, Congruence, and Similarity
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ALPObjective:

Symmetry, Congruence, and Similarity

In this lesson you will demonstrate an understanding of symmetry, congruence, and similarity.

Vocabulary:

If you need to check a word's definition, please go to the glossary by clicking the Vocabulary button

  • acute
  • angle
  • circumference
  • cone
  • cube
  • diagonal
  • diameter
  • edge
  • equilateral
  • face
  • hexagon
  • isosceles
  • obtuse
  • octagon
  • parallelogram
  • pentagon
  • perpendicular
  • pyramid
  • quadrilateral
  • rhombus
  • right angle
  • sphere
  • trapezoid
  • vertex (vertices)
  • cylinder
  • polyhedron
  • prism
  • tessellation

Tips to Remember:

Symbols

To show "congruent to":

To show a right angle:

Hash marks may be used on line segments to indicate that they are of equal length:

The inverted T is used to indicate perpendicular lines.

Triangles

The measurement of the three angles within a triangle total 180 degrees.

There are three kinds of triangles. An equilateral triangle is a triangle that has all three sides the same length. An isosceles triangle is a triangle that has two sides that are the same length. A scalene triangle is a triangle that has all three sides with a different length.

Angles

There are three kinds of angles. A right angle measures 90 degrees. An acute angle measures less than 90 degrees. An obtuse angle measures greater than 90 degrees.

Quadrilaterals

A quadrilateral is a polygon with 4 sides. Some quadrilaterals include squares, rectangles, parallelograms, and trapezoids.

Polygons

  • A polygon is a closed figure formed by line segments.
  • A regular polygon is a polygon with all sides the same length and the all angles the same measure.
  • An irregular polygon is a polygon with sides of different lengths and the angle measurements are different as well.

Congruent Figures

Figures that have the same size and shape. Figures are congruent if you can slide, flip, or turn (rotate) one to make it fit exactly on the other one.

Similar Figures

Figures that have the same shape, but necessarily don't have the same size.

Symmetry

Symmetrical or symmetry means correspondence in size, shape, and relative position of parts on opposite sides of a dividing line about an axis. To see if a figure is symmetrical, you need to find a line through the figure that when the figure is folded along that line both sides of the line are the same, they match up identically. Here are some examples of geometric figures with lines of symmetry:

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