ASVAB Preparation: Geometry Review

You will need to have a basic understanding of geometry for the ASVAB. Geometry is “the branch of mathematics that deals with the deduction of the properties, measurement, and relationships of points, lines, angles, and figures in space from their defining conditions by means of certain assumed properties of space.” Sounds interesting!

Really, geometry is simply the branch of mathematics that’s concerned with shapes, lines, and angles. From the perspective of the ASVAB math subtests, you should be able to identify basic geometric shapes and know certain properties about them so you can determine their angles and measurements. You see a lot of geometry-related questions on both the Mathematics Knowledge and the Arithmetic Reasoning subtests of the ASVAB.

Know all the angles

Angles are formed when two lines intersect at a point. Many geometric shapes are formed by intersecting lines, which form angles. Angles can be measured in degrees. The greater the number of degrees, the wider the angle is:

  • A straight line is exactly 180°.

  • A right angle is exactly 90°.

  • An acute angle is more than 0° and less than 90°.

  • An obtuse angle is more than 90° but less than 180°.

  • Complementary angles are two angles that equal 90° when added together.

  • Supplementary angles are two angles that equal 180°when added together.

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Common geometric shapes

You don’t need to know all of the geometric shapes to solve the math problems you find on the ASVAB. However, you should recognize the most common shapes associated with geometry.

Getting square with quadrilaterals

A quadrilateral is a geometric shape with four sides. All quadrilaterals contain interior angles totaling 360°. Here are the five most common types of quadrilaterals:

  • Squares have four sides of equal length, and all the angles are right angles.

  • Rectangles have all right angles.

  • Rhombuses have four sides of equal length, but the angles don’t have to be right angles.

  • Trapezoids have at least two sides that are parallel.

  • Parallelograms have opposite sides that are parallel, and their opposite sides and angles are equal.

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Trying out triangles

A triangle consists of three straight lines whose three interior angles always add up to 180°. The sides of a triangle are called legs. Triangles can be classified according to the relationship between their angles, the relationship between their sides, or some combination of these relationships. You should know the three most common types of triangles:

  • Isosceles triangle: Has two equal sides, and the angles opposite the equal sides are also equal.

  • Equilateral triangle: Has three equal sides, and all the angles measure 60°.

  • Right triangle: Has one right angle (90°); therefore, the remaining two angles are complementary (add up to 90°). The side opposite the right angle is called the hypotenuse, which is the longest side of a right triangle.

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Settling on circles

A circle is formed when the points of a closed line are all located equal distances from a point called the center of the circle. A circle always has 360°. The closed line of a circle is called its perimeter or circumference.

The radius of a circle is the measurement from the center of the circle to any point on the circumference of the circle. The diameter of the circle is measured as a line passing through the center of the circle, from a point on one side of the circle to a point on the other side of the circle. The diameter of a circle is always twice as long as the radius.

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