ACT Geometry

Even if you had a terrible Geometry teacher in 9th or 10th grade, you can still get most of the ACT Math Test Geometry questions correct with the basic information in this blog! Here are all the need-to-know definitions!

 

Common ACT Geometry Terms

Describing Angles:

Angle, Vertex

An angle is formed by two lines or line segments which intersect at one point. The point of intersection is called the vertex. Angles are measured in either degrees or radians.  A circle has 360 degrees total. You might see in your online studying questions involving radians, and some test questions will ask you to convert radians to degrees. To convert from degrees to radians, multiply by π/180.  To convert from radians to degrees multiply by 180/π.

Acute, Obtuse, Right, Straight

An acute angle is an angle whose measurement in degrees is between 0 and 90. A right angle is an angle whose measurement in degrees is exactly 90. An obtuse angle is an angle whose degree measure is between 90 and 180. A straight angle is an angle whose degree measure is exactly 180 degrees. All of the angles on one side of a straight line sum to 180 degrees. All of the angles around one point must sum to 360 degrees.

Perpendicular, Supplementary, Complementary

Perpendicular lines are formed when the angle between two lines is 90 degrees. The shortest distance from a point to a line is a line with a length such that the two lines form a 90 degree angle.

Two angles are supplementary if they share one line; i.e., if they sum of their angles is 180 degrees. Two angles are complementary if together they make a right angle; i.e., if the sum of their angles is 90 degrees.

 

Related Geometry Terms + Practice

Bisect, Transversal

To bisect an angle means to cut it in half. The two smaller angles will then have the same measurement.

If two parallel lines intersect with a third line, the third line is called a transversal. When this happens, all acute angles are equal and all obtuse angles are equal. Each acute angle is supplemental to each obtuse angle. Let’s practice with some related geometry terms:

x and y are parallel lines, and z is the transversal

a = d = e = h

c = b = g = f

Vertical

Vertical angles are a pair of opposite angles formed by intersecting lines. For the figure, a and d is an example of a pair of vertical angles. Vertical angles are equal.

Let’s try a quick practice problem using what we just learned!

ag_img1

In the figure to the left, lines d and f are parallel and the angle measures are as given. What is the value of x?

(A) 35

(B) 60

(C) 85

(D) 100

(E) 120

Since vertical angles are congruent, the angle vertical to the 35-degree angle also has a measure of 35 degrees. The supplement of the 120-degree angle has a measure of 60 degrees, so we then have a triangle with angles measuring 35, 60, and x degrees, as shown in the figure provided. Since the angles of a triangle add to 180 degrees, 35 + 60 + x = 180 and x = 180 – 35 – 60 = 85 degrees.

 

By the way, Magoosh can help you study for both the SAT and ACT exams. Click here to learn more!

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