5th Grade Geometry: Help for Struggling Students

Geometry Skills for 5th Grade

Graphing Coordinate Points

A coordinate plane is constructed from two number lines positioned perpendicularly to one another. The point where they intersect is called the origin. The horizontal number line is called the x-axis and the vertical number line is called the y-axis.

The 2-dimensional space bounded by these axes is the coordinate plane, and each coordinate point on the plane is defined by an ordered pair (x, y). The value of x in the ordered pair tells you where the point is on the coordinate plane relative to the x-axis, and the value of y describes the position of the point relative to the y-axis.

For instance, the ordered pair (2, 5) represents a coordinate point that lines up with the two on the x-axis and the five on the y-axis. Another way to think about ordered pairs is that they are directions to a point from the origin. In the case of (2, 5), you could find it by moving two spaces along the x-axis from the origin and then moving five spaces along the y-axis from that point.

Classifying Shapes

Polygons

The polygon is one of the main classifications for 2-dimensional shapes. Polygons have a finite (countable) number of straight-line sides. While circles and ovals don't fit into this category, most of the other shapes you'll encounter do. Triangles, trapezoids and pentagons are all examples of polygons.

Within the polygon category, there are many smaller groupings. For instance, any polygon that has exactly four sides is a quadrilateral. Lots of polygons, like rhombuses and rectangles, are also quadrilaterals; other polygons, like triangles and hexagons, are not.

Parallelograms

Within the quadrilateral group, there are even more specific classifications for shapes, like trapezoids, which have two parallel sides. There are also parallelograms, which have two sets of congruent, parallel sides.

More classifications can be made within the parallelogram group. For instance, rectangles are parallelograms because they have two sets of congruent, parallel sides, but they're special because they must also have four right angles. As a result, all rectangles are parallelograms, but not all parallelograms are rectangles.

Some other parallelograms fit into the rhombus category. A rhombus has two sets of congruent, parallel sides, just like a parallelogram. However, rhombuses are special because their two sets of sides are congruent to one another. In other words, they have four equal sides.

There's one more very special type of parallelogram that meets the requirements to be a rectangle and a rhombus. The square is a parallelogram that gets its own classification because it has four congruent, parallel sides (like a rhombus) and four right angles (like a rectangle).