Geometry is an important part of the ASVAB test, covering concepts such as shapes, angles, area, perimeter, and volume. To succeed in this section, you need to have a solid understanding of geometric principles and formulas. By mastering geometry concepts, you can improve your overall ASVAB score and increase your chances of qualifying for a variety of military careers. This guide will provide you with a comprehensive review of key geometry topics, along with practice questions to help you hone your skills. Whether you're brushing up on the basics or tackling more advanced problems, these resources will assist you in achieving success on the ASVAB Geometry section.

ASVAB

In the circle seen below, what is the value of x?

Given any chord, if a second chord is perpendicular to that chord and also passes through the center of the circle, then the first chord must be bisected. This means the first chord has been divided into two equal halves, meaning x must also be 8.

If two angles in a triangle measure 35 degrees and 47 degrees, what is the value of the third angle?

The interior angles of a triangle must add up to 180 degrees. 
 180 – 35 – 47 = 98 degrees. 
 Thus, the last angle in the triangle must be 98 degrees.

Lines A and B are parallel. If Angle 4 is 100 degrees, then angle 1 is <code>_________</code>.

Two angles that form a straight line add up to 180 degrees.  If Angle 4 is 100 degrees then Angle 1 must be 80 degrees.

You are told that one of the internal angles of a parallelogram is 54 degrees. This means at least one other angle must be equal to <code>_________</code>.

A parallelogram has 2 sets of angles that are equal to one another. That means if one angle is 54 degrees, at least one other angle (the opposite angle) must also be 54 degrees. The other two angles are each 126 degrees because 2 angles next to each other in a parallelogram are supplementary angles (add up to 180 degrees).

A trapezoid is a quadrilateral with one set of <code>_________</code> sides.

A trapezoid is a quadrilateral with one set of parallel sides.

The dimensions of this rectangular parallelepiped are height h = 8, length l = 4, and width w= 6. What is the volume?

The volume of a rectangular parallelepiped is height x length x width: v = hlw = 8 × 4 × 6 = 192.

Which of the following statements about a parallelogram is NOT true?

A parallelogram is a quadrilateral with two sets of parallel sides. Opposite sides (a = c, b = d) and angles (red = red, blue = blue) are equal. The area of a parallelogram is base x height and the perimeter is the sum of the lengths of all sides (a + b + c + d).

Opposite sides and adjacent angles are equal.

The area of a parallelogram is base x height.

The perimeter of a parallelogram is the sum of the lengths of all sides.

A line passes through the point (−1, 2). Which of the following CANNOT be the equation of the line?

The slope-intercept form of a line is: y=mx+b We know the line passes through (−1,2). It could have a slope, it could be vertical (x=−1), or it could be horizontal (y=2). Plug x=−1 into all four equations to see which equation is not satisfied. The only answer choice that doesn’t give us y=2 is y=x+1.

A rectangle is cut in half to create two squares, each of which has an area of 25. What is the perimeter of the original rectangle?

The formula to find the area of a square is Side × Side. If each square has an area of 25, then each side of the square must be 5 (because 5 × 5 = 25). So the dimensions of the rectangle are 5 × 10. The perimeter is the sum of all the sides and is therefore 5 + 10 + 5 + 10 = 30.

How much water could a container hold that measures 8cm by 12cm by 10cm?

The volume of the container is equal to the length times the width times the height. @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ Cubic centimeters are equal to ml, so a container with a volume of 960 cc can hold 960 ml.

Master Geometry Concepts for ASVAB Success

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Master Geometry Concepts for ASVAB Success

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