ACT For Dummies: Book + 3 Practice Tests Online + Flashcards, 7th Edition

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ACT Geometry Test: Analyzing Angles

Angle problems make up a big part of the ACT geometry test. Fortunately, understanding angles is easy when you memorize a few basic concepts. After all, you don’t have to do any proofs on the test. Finding an angle is usually a matter of simple addition or subtraction. Here are a few things you need to know about angles to succeed on the ACT:

• Angles that are greater than 0 but less than 90 degrees are called acute angles. Think of an acute angle as being a cute little angle.
• Angles that are equal to 90 degrees are called right angles. They’re formed by perpendicular lines and indicated by a box in the corner of the two intersecting lines.

Don’t automatically assume that angles that look like right angles are right angles. Without calculating the degree of the angle, you can’t know for certain that an angle is a right angle unless one of the following is true:

• • The problem directly tells you, “This is a right angle.”
  • You see the perpendicular symbol, indicating that the lines form a 90-degree angle.
  • You see a box in the angle, like the one in the following figure.
• Angles that are greater than 90 degrees but less than 180 degrees are called obtuse angles. Think of obtuse as obese; an obese (or fat) angle is an obtuse angle.
• Angles that measure exactly 180 degrees are called straight angles.

• Angles that total 90 degrees are called complementary angles. Think of C for corner (the lines form a 90-degree corner angle) and C for complementary.
• Angles that total 180 degrees are called supplementary angles. Think of S for supplementary (or straight) angles. Be careful not to confuse complementary angles with supplementary angles. If you’re likely to get them confused, just think alphabetically: C comes before S in the alphabet; 90 comes before 180 when you count.

• Angles that are greater than 180 degrees but less than 360 degrees are called reflex angles.

• Angles around a point total 360 degrees.
• The exterior angles of any figure are supplementary to the two opposite interior angles and always total 360 degrees.

• Angles that are opposite each other have equal measures and are called vertical angles. Just remember that vertical angles are across from each other, whether they’re up and down (vertical) or side by side (horizontal). (The following figure shows two sets of vertical angles.)

• Angles in the same position around two parallel lines and a transversal are called corresponding angles and have equal measures. (The following figure shows two sets of corresponding angles.)

When you see two parallel lines and a transversal (that’s the line going across the parallel lines), number the angles. Start in the upper-right corner with 1 and go clockwise. For the second batch of angles, start in the upper-right corner with 5 and go clockwise. Note that in the preceding figure, all odd-numbered angles are equal and all even-numbered angles are equal.

Be careful not to zigzag back and forth when numbering. If you zig when you should have zagged, you can no longer use the tip that all even-numbered angles are equal to one another and all odd-numbered angles are equal to one another.

ACT Articles

ACT Geometry Test: Triangle Trauma

Many of the geometry problems on the ACT require you to know a lot about triangles. Remember the facts and rules about triangles given here, and you’re on your way to acing geometry questions.

Classifying triangles

Triangles are classified based on the measurements of their sides and angles. Here are the types of triangles you may need to know for the ACT:

• Equilateral: A triangle with three equal sides and three equal angles.
• Isosceles: A triangle with two equal sides and two equal angles. The angles opposite equal sides in an isosceles triangle are also equal.
• Scalene: A triangle with no equal sides and no equal angles.

Sizing up triangles

When you’re figuring out ACT questions that deal with triangles, you need to know these rules about the measurements of their sides and angles:

• In any triangle, the largest angle is opposite the longest side.

• In any triangle, the sum of the lengths of two sides must be greater than the length of the third side.

• In any type of triangle, the sum of the interior angles is 180 degrees.

• The measure of an exterior angle of a triangle is equal to the sum of the two remote interior angles.

Zeroing in on similar triangles

Several ACT math questions require you to compare similar triangles. Similar triangles look alike but are different sizes. Here’s what you need to know about similar triangles:

• Similar triangles have the same angle measures. If you can determine that two triangles contain angles that measure the same degrees, you know the triangles are similar.
• The sides of similar triangles are in proportion. For example, if the heights of two similar triangles are in a ratio of 2:3, then the bases of those triangles are also in a ratio of 2:3.

Don’t assume that triangles are similar on the ACT just because they look similar to you. The only way you know two triangles are similar is if the test tells you they are or you can determine that their angle measures are the same.

ACT Articles

10 Ways Parents Can Help Their Kids on the ACT

As a parent, you may wonder what you can do to help your student study for the ACT. Well, wonder no longer! Here are ten specific steps for helping your child do his or her best.

Give him awesome test-prep materials

If you bought a study prep guide for your child, you did him a huge favor. Taking full-length practice tests give your child an edge over other juniors and seniors who haven’t prepared. Nicely done!

Encourage her to study

Help your child work out a study schedule and give her incentives to stick to it, such as picking out the family’s dinner menu for one week or allotting her a larger share of the family’s talk and text minutes.

Supply him with a good study environment

Make sure your student has a quiet study area where he can concentrate without being disturbed by siblings, pets, friends, TV, the computer, or his cellphone. Quality study time is time spent without distractions.

Take practice tests with her

You’ll be better able to discuss the questions and answers with your child if you take the practice tests, too. Pretend you’re a test proctor and be the official timer for your student when she takes the full-length practice tests. After she’s done, read through the answer explanation with your whiz kid and help her discover which question types she may need to improve on. Then look up those particular topics for a refresher on the rules that govern them.

Model good grammar for him

Help your child recognize mistakes in English usage questions by speaking properly with him and gently correcting his grammar mistakes in your conversations. Before you know it, he’ll be correcting you!

Help her memorize math formulas

The online Cheat Sheet has a list of tips your student needs to know for the test; check it out at Dummies.com and search for ACT Cheat Sheet. Quiz her to make sure she remembers them.

Encourage him to read

One of the best ways to improve reading scores is to actually read. Go figure! Incorporate reading into your family’s schedule and set up times to read short passages together and discuss their meanings.

Explore colleges with her

Your child’s ACT score becomes more important to her when she realizes what’s at stake. Taking her to college fairs and campus visits can foster her enthusiasm for college and make taking the ACT more relevant.

Get him to the test site on time

If the test site is unfamiliar to you, take a test drive before the exam date to make sure you don’t get lost or encounter unexpected roadwork on the morning of the test. That day, make sure your kid’s alarm is set properly so he rises with plenty of time to get dressed, eat a healthy breakfast, and confirm he has the items he needs to take with him to the exam.

Help her keep a proper perspective

Remind your student that although the ACT is important, it isn’t more important than her schoolwork or being good to her family. Her exam score isn’t a reflection of her worth (or your parenting skills). It’s just one of many tools that colleges use to assess students’ skills and determine whether they’re a proper fit for their freshman classes.