Geometry and Spatial Sense, Grades 4 to 6 - EduGains

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These two angles are congruent because they are the
same measure. The fact that the rays are different
lengths and the angles “face” opposite directions
does not affect congruence.
Shapes that are transformed by reflection, translation,
or rotation exhibit congruence. The transformed
shape is congruent to the original shape.
An understanding of congruence is beneficial when students encounter other geometric
concepts such as transformations, tiling patterns, and symmetry.
Investigating Polygon Properties
In the junior grades, students continue to develop their understanding of the properties of
two-dimensional shapes. They focus on specific shapes called polygons. A polygon is a closed
shape formed by three or more straight sides. Polygons include triangles, quadrilaterals,
octagons, and so forth.
The properties of polygons are summarized in the following table:
Number of sides One of the first properties students learn to
consider is the number of sides a shape has.
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This information allows students to identify
triangles, quadrilaterals, pentagons, hexagons,
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heptagons, octagons, and so forth. 5
Number of
vertices
Junior students should recognize that the
point at which two lines meet is called a
vertex. With experience, students will discover
that the number of vertices in a polygon is the
same as the number of sides.
Length of sides Students learn that the length of sides is an
important property of many two-dimensional
shapes. They recognize that the sides of
squares are of equal length, and that pairs
of opposite sides are equal for all other
parallelograms.
Learning About Two-Dimensional Shapes in the Junior Grades 4
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