We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

SSAT Upper Level Math : How to find if two acute / obtuse triangles are similar

Study concepts, example questions & explanations for SSAT Upper Level Math

Create An Account

All SSAT Upper Level Math Resources

6 Diagnostic Tests 311 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : How To Find If Two Acute / Obtuse Triangles Are Similar

$\bigtriangleup ABC \sim \bigtriangleup DEF$ ; AB = 24, BC = 30, AC = 36 ; $\bigtriangleup DEF$ has perimeter 400.

Which of the following is equal to $DF \div DE$ ?

Possible Answers:

1.25

1.2

1.5

$0.8\overline{3}$

$0.\overline{6}$

Correct answer:

1.5

Explanation:

The perimeter of $\bigtriangleup DEF$ is actually irrelevant to this problem. Corresponding sides of similar triangles are in proportion, so use this to calculate $DF \div DE$ , or $\frac{DF}{DE}$ :

$\frac{DF}{DE} = \frac{AC}{AB} = \frac{36}{24} = 1.5$

Report an Error

Example Question #2 : How To Find If Two Acute / Obtuse Triangles Are Similar

$\bigtriangleup ABC \sim \bigtriangleup DEF$ ; AB = 24, BC = 20, AC = 36 ; $\bigtriangleup DEF$ has perimeter 300.

Evaluate DE + EF .

Possible Answers:

225

Insufficient information is given to answer the problem.

200

165

210

Correct answer:

165

Explanation:

The ratio of the perimeters of two similar triangles is equal to the ratio of the lengths of a pair of corresponding sides. Therefore,

$\frac{DE}{AB}= \frac{P_{\bigtriangleup DEF}}{P_{\bigtriangleup ABC }}$ and $\frac{EF}{BC}= \frac{P_{\bigtriangleup DEF}}{P_{\bigtriangleup ABC }}$ , or

$\frac{DE}{AB}=\frac{EF}{BC} = \frac{P_{\bigtriangleup DEF}}{P_{\bigtriangleup ABC }}$

By one of the properties of proportions, it follows that

$\frac{DE+EF}{AB+BC} = \frac{P_{\bigtriangleup DEF}}{P_{\bigtriangleup ABC }}$

The perimeter of $\bigtriangleup ABC$ is

AB+BC+ AC = 24+ 20+ 36 = 80 , so

$\frac{DE+EF}{24+20} = \frac{300}{80}$

$\frac{DE+EF}{44} = \frac{300}{80}$

$\frac{DE+EF}{44} \cdot 44 = \frac{300}{80} \cdot 44$

DE+EF=165

Report an Error

Example Question #1 : How To Find If Two Acute / Obtuse Triangles Are Similar

$\bigtriangleup ABC \sim \bigtriangleup DEF$ ; AB= 12 ; DE = 40 ; $\bigtriangleup DEF$ has perimeter 90.

Give the perimeter of $\bigtriangleup ABC$ .

Possible Answers:

$53\frac{1}{3}$

360

300

Correct answer:

Explanation:

The ratio of the perimeters of two similar triangles is the same as the ratio of the lengths of a pair of corresponding sides. Therefore,

$\frac{P_{\bigtriangleup ABC }}{P_{\bigtriangleup DEF}} = \frac{AB}{DE}$

$\frac{P_{\bigtriangleup ABC }}{90} = \frac{12}{40}$

$\frac{P_{\bigtriangleup ABC }}{90}\cdot 90 = \frac{12}{40} \cdot 90$

$P_{\bigtriangleup ABC} = 27$

Report an Error

Example Question #2 : How To Find If Two Acute / Obtuse Triangles Are Similar

$\bigtriangleup ABC \sim \bigtriangleup DEF$ .

$m\angle A + m\angle D = 94^{\circ }$

$m\angle B + m\angle F = 94^{\circ }$

Evaluate $m \angle C + m \angle E$ .

Possible Answers:

$86^{\circ }$

$188^{\circ }$

These triangles cannot exist.

$172^{\circ }$

$94^{\circ }$

Correct answer:

$172^{\circ }$

Explanation:

The similarity of the triangles is actually extraneous information here. The sum of the measures of a triangle is $180 ^{\circ }$ , so:

$m \angle A + m \angle B + m \angle C = 180^{\circ }$

$m \angle D + m \angle E + m \angle F = 180^{\circ }$

$m \angle A + m \angle B + m \angle C +m \angle D + m \angle E + m \angle F = 180^{\circ }+ 180^{\circ }$

$m \angle C + m \angle E + (m \angle A +m \angle D) + (m \angle B + m \angle F )= 360^{\circ }$

$m \angle C + m \angle E +94 ^{\circ } +94 ^{\circ }= 360^{\circ }$

$m \angle C + m \angle E +188 ^{\circ }= 360^{\circ }$

$m \angle C + m \angle E +188 ^{\circ }- 188^{\circ } = 360^{\circ } - 188^{\circ }$

$m \angle C + m \angle E = 172^{\circ }$

Report an Error

Example Question #131 : Properties Of Triangles

Given: $\bigtriangleup ABC$ and $\bigtriangleup DEF$ ; $\angle A \cong \angle D$ and $\angle C \cong \angle F$ .

Which of the following statements would not be enough, along with what is given, to prove that $\bigtriangleup ABC \sim \bigtriangleup DEF$ ?

Possible Answers:

$\frac{AB}{DE} = \frac{BC}{EF}$

$\frac{AB}{DE} = \frac{AC}{DF}$

The given information is enough to prove the triangles similar.

$\frac{AC}{DF}= \frac{BC}{EF}$

$\angle B \cong \angle E$

Correct answer:

The given information is enough to prove the triangles similar.

Explanation:

Two pairs of corresponding angles are stated to be congruent in the main body of the problem; it follows from the Angle-Angle Similarity Postulate that the triangles are similar. No further information is needed.

Report an Error

Example Question #132 : Properties Of Triangles

$\bigtriangleup ABC \sim \bigtriangleup DEF$ . $\frac{AB}{DE} = \frac{25}{36}$ . Which of the following is the ratio of the area of $\bigtriangleup DEF$ to that of $\bigtriangleup ABC$ ?

Possible Answers:

$\frac{625}{1,296}$

$\frac{6}{5}$

$\frac{1,296}{625}$

$\frac{36}{25}$

$\frac{5}{6}$

Correct answer:

$\frac{1,296}{625}$

Explanation:

The similarity ratio of $\bigtriangleup ABC$ to $\bigtriangleup DEF$ is equal to the ratio of two corresponding sidelengths, which is given as $\frac{25}{36}$ ; the similarity ratio of $\bigtriangleup DEF$ to $\bigtriangleup ABC$ is the reciprocal of this, or $\frac{36}{25}$ .

The ratio of the area of a figure to that of one to which it is similar is the square of the similarity ratio, so the ratio of the area of $\bigtriangleup DEF$ to that of $\bigtriangleup ABC$ is

$\left (\frac{36}{25} \right ) ^{2}= \frac{1,296}{625}$

Report an Error

Example Question #5 : How To Find If Two Acute / Obtuse Triangles Are Similar

$\bigtriangleup ABC \sim \bigtriangleup DEF$ ; $m \angle D = 44 ^{\circ }, m \angle E = 26^{\circ }$

Which of the following is true about $\bigtriangleup ABC$ ?

Possible Answers:

$\bigtriangleup ABC$ is scalene and acute.

None of the other responses is correct.

$\bigtriangleup ABC$ is isosceles and acute.

$\bigtriangleup ABC$ is scalene and obtuse.

$\bigtriangleup ABC$ is isosceles and obtuse.

Correct answer:

$\bigtriangleup ABC$ is scalene and obtuse.

Explanation:

Corresponding angles of similar triangles are congruent, so the measures of the angles of $\bigtriangleup ABC$ are equal to those of $\bigtriangleup DEF$ .

Two of the angles of $\bigtriangleup DEF$ have measures $44 ^{\circ }$ and $26^{\circ }$ ; its third angle measures

$180^{\circ } - (44^{\circ }+ 26^{\circ } ) = 180^{\circ } - 70 ^{\circ } = 110^{\circ }$ .

One of the angles having measure greater than $90^{\circ }$ makes $\bigtriangleup DEF$ - and, consequently, $\bigtriangleup ABC$ - an obtuse triangle. Also, the three angles have different measures, so the sides do as well, making $\bigtriangleup ABC$ scalene.

Report an Error

Example Question #133 : Properties Of Triangles

$\bigtriangleup ABC \sim \bigtriangleup DEF$ ; $m \angle A = 66^{\circ }$ ; $m \angle F = 63^{\circ }$ .

Which of the following correctly gives the relationship of the angles of $\bigtriangleup ABC$ ?

Possible Answers:

$m \angle C =m \angle B < m \angle A$

$m \angle C <m \angle B = m \angle A$

$m \angle C <m \angle B < m \angle A$

$m \angle B < m \angle C <m \angle A$

$m \angle B = m \angle C <m \angle A$

Correct answer:

$m \angle B < m \angle C <m \angle A$

Explanation:

$m \angle A = 66^{\circ }$

Corresponding angles of similar triangles are congruent, so $m \angle C =m \angle F = 63^{\circ }$ .

Consequently,

$m \angle B = 180^{\circ } - (m \angle A +m \angle C)$

$m \angle B = 180^{\circ } - ( 66^{\circ }+ 63^{\circ })$

$m \angle B = 180^{\circ } - 129^{\circ } = 51^{\circ }$

Therefore,

$m \angle B < m \angle C <m \angle A$ .

Report an Error

Example Question #3 : How To Find If Two Acute / Obtuse Triangles Are Similar

$\bigtriangleup ABC \sim \bigtriangleup DEF$ ; AB = 50, BC = DE= 75, DF = 100 .

Which of the following correctly gives the relationship of the angles of $\bigtriangleup ABC$ ?

Possible Answers:

$m \angle C< m \angle A <m \angle B$

$m \angle A <m \angle B < m \angle C$

$m \angle B < m \angle C < m \angle A$

$m \angle C <m \angle B < m \angle A$

$m \angle B < m \angle A < m \angle C$

Correct answer:

$m \angle C <m \angle B < m \angle A$

Explanation:

Corresponding sides of similar triangles are in proportion; since $\bigtriangleup ABC \sim \bigtriangleup DEF$ ,

$\frac{AC}{DF} = \frac{AB}{DE}$

$\frac{AC}{100} = \frac{50}{75}$

$\frac{AC}{100} \cdot 100 = \frac{50}{75} \cdot 100$

$AC = 66\frac{2}{3}$

Therefore, AB < AC < BC .

The angle opposite the longest (shortest) side of a triangle is the angle of greatest (least) measure, so

$m \angle C <m \angle B < m \angle A$ .

Report an Error

Example Question #141 : Properties Of Triangles

$\bigtriangleup ABC \sim \bigtriangleup DEF \sim \bigtriangleup GHI$ .

AB = DF=HI = 24

AC = 32

GH = 40

Order the triangles by perimeter, least to greatest.

Possible Answers:

$\bigtriangleup DEF, \bigtriangleup ABC,\bigtriangleup GHI$

$\bigtriangleup ABC, \bigtriangleup GHI,\bigtriangleup DEF$

$\bigtriangleup GHI,\bigtriangleup DEF,\bigtriangleup ABC$

$\bigtriangleup ABC,\bigtriangleup DEF, \bigtriangleup GHI$

$\bigtriangleup DEF,\bigtriangleup GHI, \bigtriangleup ABC$

Correct answer:

$\bigtriangleup DEF, \bigtriangleup ABC,\bigtriangleup GHI$

Explanation:

$\overline{DF}$ and $\overline{AC}$ are corresponding sides of their respective triangles, and DF < AC , so it easily follows from proportionality that each side of $\bigtriangleup DEF$ is shorter than its corresponding side in $\bigtriangleup ABC$ . Therefore, $\bigtriangleup DEF$ is of lesser perimeter than $\bigtriangleup ABC$ . By the same reasoning, since AB < GH , $\bigtriangleup ABC$ is of lesser perimeter than $\bigtriangleup GHI$ .

The correct response is

$\bigtriangleup DEF, \bigtriangleup ABC,\bigtriangleup GHI$

Report an Error

View SSAT- Upper Level Tutors

Gregory
Certified Tutor

Pennsylvania State University-Main Campus, Bachelor of Science, Chemical Engineering. Carnegie Mellon University, Doctor of P...

View SSAT- Upper Level Tutors

Christie
Certified Tutor

Elizabeth City State University, Bachelor of Education, Education. Gardner-Webb University, Masters in Education, Educational...

View SSAT- Upper Level Tutors

Cynthia
Certified Tutor

Arizona State University, Bachelors, Psychology. Arizona State University, Master in Public Health, Psychology.

All SSAT Upper Level Math Resources

6 Diagnostic Tests 311 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

SSAT Tutors in Atlanta, Spanish Tutors in New York City, Computer Science Tutors in Denver, SAT Tutors in New York City, SSAT Tutors in Denver, GRE Tutors in Chicago, Physics Tutors in Phoenix, GRE Tutors in Boston, SSAT Tutors in Boston, Biology Tutors in Boston

Popular Courses & Classes

ACT Courses & Classes in Philadelphia, LSAT Courses & Classes in San Francisco-Bay Area, ACT Courses & Classes in Houston, SSAT Courses & Classes in Miami, MCAT Courses & Classes in Los Angeles, SSAT Courses & Classes in Boston, GMAT Courses & Classes in Washington DC, Spanish Courses & Classes in Houston, ISEE Courses & Classes in Washington DC, MCAT Courses & Classes in Phoenix

Popular Test Prep

GRE Test Prep in Philadelphia, MCAT Test Prep in Dallas Fort Worth, SSAT Test Prep in Washington DC, GMAT Test Prep in San Diego, SSAT Test Prep in Miami, SAT Test Prep in Atlanta, SAT Test Prep in Philadelphia, GMAT Test Prep in Washington DC, GMAT Test Prep in San Francisco-Bay Area, MCAT Test Prep in Houston

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)

HIGH SCHOOL

GRADUATE SCHOOL

K-8

Search 50+ Tests

math tutoring

science tutoring

foreign languages

elementary tutoring

other

Search 350+ Subjects

SSAT Upper Level Math : How to find if two acute / obtuse triangles are similar

Study concepts, example questions & explanations for SSAT Upper Level Math

All SSAT Upper Level Math Resources

Example Questions

Example Question #1 : How To Find If Two Acute / Obtuse Triangles Are Similar

Example Question #2 : How To Find If Two Acute / Obtuse Triangles Are Similar

Example Question #1 : How To Find If Two Acute / Obtuse Triangles Are Similar

Example Question #2 : How To Find If Two Acute / Obtuse Triangles Are Similar

Example Question #131 : Properties Of Triangles

Example Question #132 : Properties Of Triangles

Example Question #5 : How To Find If Two Acute / Obtuse Triangles Are Similar

Example Question #133 : Properties Of Triangles

Example Question #3 : How To Find If Two Acute / Obtuse Triangles Are Similar

Example Question #141 : Properties Of Triangles

All SSAT Upper Level Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: