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

Study concepts, example questions & explanations for GMAT Math

Create An Account

All GMAT Math Resources

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

Example Questions

Example Question #2 : Triangles

Which of two triangles has greater area, $\Delta ABC$ or $\Delta DEF$ ?

Statement 1: $\angle A \cong \angle D; \angle B \cong \angle E$

Statement 2: $AB = 1.1 \cdot DE$

Possible Answers:

EITHER statement ALONE is sufficient to answer the question.

BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.

Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.

BOTH statements TOGETHER are insufficient to answer the question.

Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.

Correct answer:

BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.

Explanation:

Statement 1 alone proves that $\Delta ABC \sim \Delta DEF$ by the Angle-Angle Postulate, but does not prove anything about the sides, which would be needed to answer this question. Statement 2 alone only gives a relationship between one side of each triangle; without any further information, this is insufficient.

The two statements together, however, present sufficient evidence. Statement 1 proves that the triangles are similar. Statement 2 gives the ratio of one side in $\Delta ABC$ to the corresponding side in $\Delta DEF$ , so, as the triangles are similar, this ratio is shared by all three pairs of corresponding sides. Since

$\frac{AB }{DE}= 1.1$ ,

1.1 is this common ratio, and the ratio of the area of $\Delta ABC$ to $\Delta DEF$ is $1.1^{2} = 1.21$ , making $\Delta ABC$ the larger triangle.

Report an Error

Example Question #3 : Triangles

True or false:

$\Delta ABC \sim \Delta DE F$

Statement 1: $\frac{AB }{DE}= \frac{BC }{EF}$

Statement 2: $\angle A \cong \angle D$ and $\angle B \cong \angle E$

Possible Answers:

Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.

BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.

BOTH statements TOGETHER are insufficient to answer the question.

Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.

EITHER statement ALONE is sufficient to answer the question.

Correct answer:

Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.

Explanation:

Statement 1 alone gives a proportion between two pairs of corresponding sides of the triangles. This is not enough to prove the triangles similar without the third side proportionality (SSS Simiilarity statement) or the congruence of the included angles (SAS Similarity statement).

Statement 2 gives two congruencies between corresponding angles, which by the Angle-Angle statement is enough to prove the triangles similar.

Report an Error

All GMAT Math Resources

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

Popular Subjects

Spanish Tutors in Philadelphia, GMAT Tutors in Chicago, ACT Tutors in Denver, Statistics Tutors in San Francisco-Bay Area, Computer Science Tutors in San Francisco-Bay Area, MCAT Tutors in Atlanta, Calculus Tutors in Washington DC, Chemistry Tutors in Washington DC, MCAT Tutors in New York City, Computer Science Tutors in Seattle

Popular Courses & Classes

SAT Courses & Classes in Seattle, ACT Courses & Classes in Dallas Fort Worth, SSAT Courses & Classes in San Francisco-Bay Area, Spanish Courses & Classes in Phoenix, GRE Courses & Classes in Denver, GRE Courses & Classes in San Francisco-Bay Area, SAT Courses & Classes in Los Angeles, GMAT Courses & Classes in Washington DC, MCAT Courses & Classes in New York City, LSAT Courses & Classes in New York City

Popular Test Prep

GRE Test Prep in Seattle, GRE Test Prep in San Francisco-Bay Area, GMAT Test Prep in Washington DC, MCAT Test Prep in Los Angeles, ACT Test Prep in Dallas Fort Worth, GMAT Test Prep in Phoenix, GMAT Test Prep in Atlanta, LSAT Test Prep in San Francisco-Bay Area, GMAT Test Prep in Seattle, SAT 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 : DSQ: Calculating if two acute / obtuse triangles are similar

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

Example Questions

Example Question #2 : Triangles

Example Question #3 : Triangles

All GMAT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details