We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

ISEE Upper Level Math : Geometry

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

Create An Account

All ISEE Upper Level Math Resources

6 Diagnostic Tests 244 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : How To Find An Angle In An Acute / Obtuse Triangle

Triangle 2

Refer to the above figure. Express in terms of .

Possible Answers:

$y =\frac{1}{3} x - 8$

$y =\frac{1}{3} x + 8$

y = x - 98

y = x - 82

Correct answer:

y = x - 98

Explanation:

The measure of an interior angle of a triangle is equal to 180 degrees minus that of its adjacent exterior angle, so

$m \angle ABC = (180 - 82)^{\circ } = 98^{\circ }$

and

$m \angle ACB = (180 - x)^{\circ }$ .

The sum of the degree measures of the three interior angles is 180, so

$m \angle BAC + m \angle ABC +m \angle ACB = 180 ^{\circ }$

y + 98 +(180 -x) = 180

y -x + 278 = 180

y -x + 278 +x - 278 = 180 +x - 278

y = 180 +x - 278

y = x - 98

Report an Error

Example Question #2 : How To Find An Angle In An Acute / Obtuse Triangle

Triangle 3

In the above figure, $\overline{AC} \cong \overline{AD}$ .

Give the measure of $\angle CAD$ .

Possible Answers:

$40 ^{\circ }$

$36 ^{\circ }$

$32 ^{\circ }$

$42^{\circ }$

Correct answer:

$36 ^{\circ }$

Explanation:

$\angle BCA$ and $\angle ACD$ form a linear pair, so their degree measures total $180 ^{\circ }$ ; consequently,

$m \angle ACD = 180 ^{\circ } - m \angle CAD$

$= 180 ^{\circ } - 108 ^{\circ }$

$= 72 ^{\circ }$

$\overline{AC} \cong \overline{AD}$ , so by the Isosceles Triangle Theorem,

$m \angle ADC = m \angle ACD = 72 ^{\circ }$

The sum of the degree measures of a triangle is $180^{\circ }$ , so

$\angle CAD + m \angle ADC + m \angle ACD = 180 ^{\circ }$

$\angle CAD + 72^{\circ } +72^{\circ } = 180 ^{\circ }$

$\angle CAD +144^{\circ } = 180 ^{\circ }$

$\angle CAD = 36 ^{\circ }$

Report an Error

Example Question #3 : How To Find An Angle In An Acute / Obtuse Triangle

Triangle

Figure NOT drawn to scale.

Refer to the above figure. Evaluate $m \angle ACB$ .

Possible Answers:

$107^{\circ }$

$102 ^{\circ }$

$112^{\circ }$

$97^{\circ }$

Correct answer:

$102 ^{\circ }$

Explanation:

The measure of an exterior angle of a triangle, which here is $\angle ACD$ , is equal to the sum of the measures of its remote interior angles, which here are $\angle A$ and $\angle B$ . Consequently,

$m \angle A + m \angle B = m \angle ACD$

(4x-2)+(2x+8) = 6.5x

4x+2x-2+8 = 6.5x

6x+6 = 6.5x

6x+6 - 6x = 6.5x - 6x

6 = 0.5x

$6 \cdot 2 = 0.5x \cdot 2$

12 = x

$m \angle ACD =( 6.5 x) ^{\circ }= (6.5 \cdot 12 )^{\circ }= 78^{\circ }$

$\angle ACB$ and $\angle ACD$ form a linear pair and, therefore,

$m \angle ACB=180 ^{\circ } - m \angle ACD = 180 ^{\circ } -78^{\circ } = 102 ^{\circ }$ .

Report an Error

Example Question #51 : Triangles

Exterior_angle

Note: Figure NOT drawn to scale.

What is the measure of angle

Possible Answers:

y = 129

y = 152

y = 142

y = 134

y = 124

Correct answer:

y = 124

Explanation:

The two angles at bottom are marked as congruent. One forms a linear pair with a $152 ^{\circ }$ angle, so it is supplementary to that angle, making its measure $(180-152)^{\circ } = 28^{\circ }$ . Therefore, each marked angle measures $28^{\circ }$ .

The sum of the measures of the interior angles of a triangle is $180^{\circ }$ , so:

y + 28 + 28 = 180

y +56= 180

y +56-56 = 180-56

y = 124

Report an Error

Example Question #91 : Plane Geometry

Which of the following is true about a triangle with two angles that measure $120^{\circ }$ and $90^{\circ }$ ?

Possible Answers:

This triangle is scalene and obtuse.

This triangle is isosceles and right.

This triangle is scalene and right.

This triangle is isosceles and obtuse.

This triangle cannot exist.

Correct answer:

This triangle cannot exist.

Explanation:

A triangle must have at least two acute angles; however, a triangle with angles that measure $120^{\circ }$ and $90^{\circ }$ could have at most one acute angle, an impossible situation. Therefore, this triangle is nonexistent.

Report an Error

Example Question #91 : Plane Geometry

Two sides of a scalene triangle measure 4 centimeters and 7 centimeters, and their corresponding angle measures 30 degrees. Find the area of the triangle.

Possible Answers:

$10\ cm^2$

$5\ cm^2$

$8\ cm^2$

$7\ cm^2$

Correct answer:

$7\ cm^2$

Explanation:

$Area=\frac{1}{2}absinC$ ,

where and are the lengths of two sides and is the angle measure.

Plug in our given values:

$Area=\frac{1}{2}absinC=\frac{1}{2}\times 4\times 7\times sin30^{\circ}$

$sin30^{\circ}=\frac{1}{2}\Rightarrow Area=\frac{1}{2}\times 4\times 7\times \frac{1}{2}=7\ cm^2$

Report an Error

Example Question #92 : Isee Upper Level (Grades 9 12) Mathematics Achievement

A scalene triangle has a base length and a corresponding altitude of . Give the area of the triangle in terms of .

Possible Answers:

t^2

4t^2

2t^2

Correct answer:

2t^2

Explanation:

$Area =\frac{bh}2{}$ ,

where is the base and is the altitude.

$Area =\frac{bh}2{}=\frac{t\times 4t}{2}=2t^2$

Report an Error

Example Question #14 : Acute / Obtuse Triangles

What is the area of a triangle on the coordinate plane with its vertices on the points (0,-4) ,(0,9), (6,7) ?

Possible Answers:

$40 \frac{1}{2}$

Correct answer:

Explanation:

The base can be seen as the (vertical) line segment connecting (0,-4) and (0,9) , which has length 9 - (-4) = 13 . The height is the pependicular distance from (6,7) to the segment; since the segment is part of the -axis, this altitude is horizontal and has length equal to -coordinate .

The area of this triangle is therefore

$A = \frac{1}{2} bh = \frac{1}{2} \cdot13 \cdot 6 = 39$ .

Report an Error

Example Question #15 : Acute / Obtuse Triangles

What is the area of a triangle on the coordinate plane with its vertices on the points (-5,0), (10,0), (6,8) ?

Possible Answers:

120

Correct answer:

Explanation:

The base can be seen as the (horizontal) line segment connecting $\left (-5,0 \right )$ and $\left (10,0 \right )$ , the length of which is 10 - (-5) = 15 . The height is the pependicular distance from (6,8) to the segment; since the segment is part of the -axis, this altitude is vertical and has a length equal to -coordinate .

The area of this triangle is therefore

$A = \frac{1}{2} bh = \frac{1}{2} \cdot15 \cdot 8 = 60$ .

Report an Error

Example Question #16 : Acute / Obtuse Triangles

Right triangle

Figure NOT drawn to scale.

$\bigtriangleup ABC$ is a right triangle with altitude $\overline{BX}$ . What percent of $\bigtriangleup ABC$ has been shaded gray?

Choose the closest answer.

Possible Answers:

$30 \%$

$25 \%$

$20 \%$

$35 \%$

Correct answer:

$25 \%$

Explanation:

The altitude of a right triangle from the vertex of its right angle - which, here, is $\overline{BX}$ - divides the triangle into two triangles similar to each other as well as the large triangle.

The similarity ratio of $\bigtriangleup AXB$ to $\bigtriangleup ABC$ is the ratio of the lengths of their hypotenuses. The hypotenuse of the latter is 18; that of the former, from the Pythagorean Theorem, is

$\sqrt{18 ^{2}+ 30 ^{2}} = \sqrt{324+ 900} = \sqrt{1,224}$

The similarity ratio is therefore $\frac{18}{ \sqrt{1,224}}$ . The ratio of their areas is the square of this, or

$\left (\frac{18}{ \sqrt{1,224}} \right )^{2} = \frac{324}{1,224} = \frac{324 \div 36 }{1,224\div 36} = \frac{9}{34}$

The area of $\bigtriangleup AXB$ is

$\frac{9}{34} \times 100 \% \approx 26.5 \%$

of that of $\bigtriangleup ABC$ , so the choice closest to the correct percent is 25%.

Report an Error

View Tutors

Latasha
Certified Tutor

Saint Joseph's University, Master of Science, Education.

View Tutors

Reza
Certified Tutor

University of Sherbrooke, Doctor of Philosophy, Mathematics. University of Manitoba, Master of Science, Mathematics.

View Tutors

Magda
Certified Tutor

Heritage College, Bachelor of Science, Education.

All ISEE Upper Level Math Resources

6 Diagnostic Tests 244 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

ISEE Tutors in Denver, GMAT Tutors in Seattle, Physics Tutors in Phoenix, Math Tutors in Seattle, Calculus Tutors in San Diego, SAT Tutors in Atlanta, ACT Tutors in Miami, English Tutors in Phoenix, Biology Tutors in Houston, SAT Tutors in Phoenix

Popular Courses & Classes

ACT Courses & Classes in Phoenix, SSAT Courses & Classes in Seattle, SSAT Courses & Classes in San Diego, SAT Courses & Classes in Chicago, GRE Courses & Classes in San Diego, GMAT Courses & Classes in Denver, SSAT Courses & Classes in Houston, LSAT Courses & Classes in Washington DC, ISEE Courses & Classes in Seattle, SAT Courses & Classes in Miami

Popular Test Prep

GRE Test Prep in Phoenix, GRE Test Prep in San Francisco-Bay Area, ISEE Test Prep in Seattle, SAT Test Prep in San Diego, SAT Test Prep in San Francisco-Bay Area, ACT Test Prep in Phoenix, SAT Test Prep in Boston, MCAT Test Prep in Houston, ACT Test Prep in New York City, SSAT Test Prep in Seattle

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

ISEE Upper Level Math : Geometry

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

All ISEE Upper Level Math Resources

Example Questions

Example Question #1 : How To Find An Angle In An Acute / Obtuse Triangle

Example Question #2 : How To Find An Angle In An Acute / Obtuse Triangle

Example Question #3 : How To Find An Angle In An Acute / Obtuse Triangle

Example Question #51 : Triangles

Example Question #91 : Plane Geometry

Example Question #91 : Plane Geometry

Example Question #92 : Isee Upper Level (Grades 9 12) Mathematics Achievement

Example Question #14 : Acute / Obtuse Triangles

Example Question #15 : Acute / Obtuse Triangles

Example Question #16 : Acute / Obtuse Triangles

All ISEE Upper Level Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: