GMAT Math : Calculating if two acute / obtuse triangles are similar

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

22 Diagnostic Tests 693 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : Calculating If Two Acute / Obtuse Triangles Are Similar

$\Delta ABC$ is an equilateral triangle. Points D,E,F are the midpoints of $\overline{AB},\overline{BC},\overline{AC}$ , respectively. $\Delta DEF$ is constructed.

All of the following are true except:

Possible Answers:

The area of $\Delta A BC$ is twice that of $\Delta DEF$ .

All of the statements in the other four choices are correct.

The perimeter of $\Delta A BC$ is twice that of $\Delta DEF$ .

$\Delta A BC \sim \Delta DEF$

Each side of $\Delta A BC$ is parallel to a side of $\Delta DEF$ .

Correct answer:

The area of $\Delta A BC$ is twice that of $\Delta DEF$ .

Explanation:

The three sides of $\Delta DEF$ are the midsegments of $\Delta A BC$ , so $\Delta DEF$ is similar to $\Delta A BC$ .

By the Triangle Midsegment Theorem, each is parallel to one side of $\Delta A BC$ .

By the same theorem, each has length exactly half of that side, giving $\Delta A BC$ twice the perimeter of $\Delta DEF$ .

But since the sides of $\Delta A BC$ have twice the length of those of $\Delta DEF$ , the area of $\Delta A BC$ , which varies directly as the square of a sidelength, must be four times that of $\Delta DEF$ .

The correct choice is the one that asserts that the area of $\Delta A BC$ is twice that of $\Delta DEF$ .

Report an Error

Example Question #2 : Calculating If Two Acute / Obtuse Triangles Are Similar

$\Delta ABC \sim \Delta D EF$

AB = 43, BC = 45, AC = 53 .

Order the angles of $\Delta D EF$ from least to greatest measure.

Possible Answers:

$\angle F, \angle E, \angle D$

$\angle E, \angle D, \angle F$

The angles of $\Delta D EF$ cannot be ordered from the information given.

$\angle E, \angle F, \angle D$

$\angle F, \angle D, \angle E$

Correct answer:

$\angle F, \angle D, \angle E$

Explanation:

In a triangle, the angle of greatest measure is opposite the side of greatest measure, and the angle of least measure is opposite the side of least measure. AB < BC < AC , so their opposite angles are ranked in this order - that is, $m \angle C < m \angle A < m \angle B$ .

Corresponding angles of similar triangles are congruent, so, since $\Delta ABC \sim \Delta D EF$ , $m \angle A= m \angle D , m \angle B= m \angle E, m \angle C = m \angle F$ .

Therefore, by substitution, $m \angle F < m \angle D < m \angle E$ .

Report an Error

Example Question #1 : Calculating If Two Acute / Obtuse Triangles Are Similar

The triangles are similar. What is the value of x?

Possible Answers:

$Not\ enough\ information$

Correct answer:

Explanation:

The proportions of corresponding sides of similar triangles must be equal. Therefore, $\small \frac{8}{12}\ =\ \frac{10}{x}$ . $\small 8x\ =\ 120; x\ =\ 15$ .

Report an Error

All GMAT Math Resources

22 Diagnostic Tests 693 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Calculus Tutors in Dallas Fort Worth, Reading Tutors in New York City, SAT Tutors in New York City, SSAT Tutors in Los Angeles, Calculus Tutors in San Francisco-Bay Area, Reading Tutors in Dallas Fort Worth, SAT Tutors in San Francisco-Bay Area, French Tutors in Miami, French Tutors in Chicago, Algebra Tutors in Miami

Popular Courses & Classes

Spanish Courses & Classes in San Diego, Spanish Courses & Classes in Boston, LSAT Courses & Classes in Philadelphia, Spanish Courses & Classes in San Francisco-Bay Area, GMAT Courses & Classes in Phoenix, GMAT Courses & Classes in New York City, MCAT Courses & Classes in Seattle, GMAT Courses & Classes in Seattle, Spanish Courses & Classes in Miami, ACT Courses & Classes in New York City

Popular Test Prep

MCAT Test Prep in Los Angeles, SSAT Test Prep in Phoenix, ISEE Test Prep in Philadelphia, ACT Test Prep in New York City, SAT Test Prep in Philadelphia, LSAT Test Prep in Philadelphia, GRE Test Prep in Philadelphia, SSAT Test Prep in Los Angeles, ISEE Test Prep in Atlanta, GRE Test Prep in San Diego

DMCA Complaint

If you believe that content available by means of the Website (as defined in our Terms of Service) infringes one or more of your copyrights, please notify us by providing a written notice (“Infringement Notice”) containing the information described below to the designated agent listed below. If Varsity Tutors takes action in response to an Infringement Notice, it will make a good faith attempt to contact the party that made such content available by means of the most recent email address, if any, provided by such party to Varsity Tutors.

Your Infringement Notice may be forwarded to the party that made the content available or to third parties such as ChillingEffects.org.

Please be advised that you will be liable for damages (including costs and attorneys’ fees) if you materially misrepresent that a product or activity is infringing your copyrights. Thus, if you are not sure content located on or linked-to by the Website infringes your copyright, you should consider first contacting an attorney.

Please follow these steps to file a notice:

You must include the following:

A physical or electronic signature of the copyright owner or a person authorized to act on their behalf; An identification of the copyright claimed to have been infringed; A description of the nature and exact location of the content that you claim to infringe your copyright, in \ sufficient detail to permit Varsity Tutors to find and positively identify that content; for example we require a link to the specific question (not just the name of the question) that contains the content and a description of which specific portion of the question – an image, a link, the text, etc – your complaint refers to; Your name, address, telephone number and email address; and A statement by you: (a) that you believe in good faith that the use of the content that you claim to infringe your copyright is not authorized by law, or by the copyright owner or such owner’s agent; (b) that all of the information contained in your Infringement Notice is accurate, and (c) under penalty of perjury, that you are either the copyright owner or a person authorized to act on their behalf.

Send your complaint to our designated agent at:

Charles Cohn Varsity Tutors LLC
101 S. Hanley Rd, Suite 300
St. Louis, MO 63105

Or fill out the form below:

Do not fill in this field

Contact Information

* Full legal name

Company name

* Phone number

* Email address

Address

* Address1

Address2

* City

* State

* Zipcode

* Country

Complaint Details

* URL of copyrighted work (where your original material is located)

* Please describe the copyrighted work so that it may be easily identified

I am the owner, or an agent authorized to act on behalf of the owner of an exclusive right that is allegedly infringed.

I have a good faith belief that the use of the material in the manner complained of is not authorized by the copyright owner, its agent, or the law.

This notification is accurate.

I acknowledge that there may be adverse legal consequences for making false or bad faith allegations of copyright infringement by using this process.

* Signature (your digital signature is legally binding)

Email address:
Your name:
Feedback:

GMAT Math : Calculating if two acute / obtuse triangles are similar

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

Example Questions

Example Question #1 : Calculating If Two Acute / Obtuse Triangles Are Similar

Example Question #2 : Calculating If Two Acute / Obtuse Triangles Are Similar

Example Question #1 : Calculating If Two Acute / Obtuse Triangles Are Similar

All GMAT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details