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Geometry and Measurement Conversions Study Guide

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Updated on Aug 24, 2011

Find practice problems and solutions for these concepts at Geometry and Measurement Conversions Practice Problems.

What's Around The Bend

  • Polygons
  • Classifying Triangles
  • Classifying Quadrilaterals
  • Perimeter
  • Area
  • Circles
  • Pythagorean Theorem
  • Volume
  • Measurement Conversions

Polygons

Plane figures are two-dimensional objects that reside on a plane. You can think of a plane like a sheet of paper that extends forever in all directions. Special figures are called polygons, several of which are defined here.

Fuel for Thought

Some important words to know:

      A polygon is a closed plane figure made up of line segments.
      A triangle is a polygon with three sides.
      A quadrilateral is a polygon with four sides.
      A pentagon is a polygon with five sides.
      A hexagon is a polygon with six sides.
      An octagon is a polygon with eight sides.

Polygons are made up of angles and line segments called sides. Each angle is made up of two sides, and the point at which they meet is called the vertex.

Triangles

Triangles are three-sided polygons. Triangles are classified, or grouped, in two different ways. One classification distinguishes by the sides, and another by the angles. For a triangle, you can have all three sides congruent (equal measure), two sides congruent, or no sides congruent.

Equilateral

Isoceles

Scalene

In triangle figures, the little box drawn inside an angle stands for a right angle (90°). Here is the classification for triangles when grouped by angle:

Acute

Right

Obtuse

Note that even though right triangles and obtuse triangles each have two acute angles, their classification is not affected by these angles. Acute triangles have all THREE acute angles.

Quadrilaterals

Four-sided polygons are called quadrilaterals, and like triangles, there are classifications for quadrilaterals.

A quadrilateral with one pair of parallel sides (bases) is called a trapezoid. In an isosceles trapezoid, the sides that are not bases are congruent. Because the parallel bases are not the same length in a trapezoid, we call these bases b1 and b2.

A quadrilateral with two pairs of parallel sides is called a parallelogram.

The two sets of opposite sides that are parallel are congruent in a parallelogram, as shown in the figure:

Quadrilaterals

Parallelograms are broken down into further subgroups.

A rectangle is a parallelogram with four right angles.

Quadrilaterals

A rhombus is a parallelogram with four congruent sides.

Quadrilaterals

A square is a parallelogram with both four right angles and four congruent sides.

Quadrilaterals

Perimeter

Perimeter is the measure AROUND a polygon. Perimeter is an addition concept; it is a linear, one-dimensional measurement.

To find the perimeter of a polygon, add up all of the lengths of the sides of the figure. Be sure to name the units.

PERIMETER

Inside Track

For a rectangle, perimeter can be found using the formula P = 2l + 2w, where P is the perimeter, l is the length, and w is the width.

For a square, or any rhombus, the perimeter can be found by P = 4s, where P is the perimeter and s is the length of one of the sides.

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