Call Now to Set Up Tutoring:

(888) 888-0446

HSPT Math : Geometry

Study concepts, example questions & explanations for HSPT Math

Create An Account

All HSPT Math Resources

6 Diagnostic Tests 130 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #781 : New Sat

A student creates a challenge for his friend. He first draws a square, the adds the line for each of the 2 diagonals. Finally, he asks his friend to draw the circle that has the most intersections possible.

How many intersections will this circle have?

Possible Answers:

Correct answer:

Explanation:

Report an Error

Example Question #1 : Geometry

Two pairs of parallel lines intersect:

Screen_shot_2013-03-18_at_10.29.11_pm

If A = 135^o, what is 2*|B-C| = ?

Possible Answers:

170°

160°

150°

140°

180°

Correct answer:

180°

Explanation:

By properties of parallel lines A+B = 180^o, B = 45^o, C = A = 135^o, so 2*|B-C| = 2* |45-135| = 180^o

Report an Error

Example Question #1 : Geometry

Lines and are parallel. $\angle HFC=10^{\circ}$ , $\angle DGI=50^{\circ}$ , $\triangle EFG$ is a right triangle, and $\overline{EG}$ has a length of 10. What is the length of $\overline{EF}$

Possible Answers:

Not enough information.

Correct answer:

Explanation:

Since we know opposite angles are equal, it follows that angle $\angle AFE=10^{\circ}$ and $\angle BGE=50^{\circ}$ .

Imagine a parallel line passing through point . The imaginary line would make opposite angles with $\angle AFE$ & $\angle BGE$ , the sum of which would equal $\angle FEG$ . Therefore, $\angle FEG=60^{\circ}$ .

$\cos (60)=.5=\frac{EG}{EF}\rightarrow EF=\frac{EG}{.5}=20$

Report an Error

Example Question #1 : Plane Geometry

If $\angle A$ measures $(40-10x)^{\circ}$ , which of the following is equivalent to the measure of the supplement of $\angle A$ ?

Possible Answers:

$(50-10x)^{\circ}$

$(10x+50)^{\circ}$

$(10x+140)^{\circ}$

$(100x)^{\circ}$

$(140-10x)^{\circ}$

Correct answer:

$(10x+140)^{\circ}$

Explanation:

When the measure of an angle is added to the measure of its supplement, the result is always 180 degrees. Put differently, two angles are said to be supplementary if the sum of their measures is 180 degrees. For example, two angles whose measures are 50 degrees and 130 degrees are supplementary, because the sum of 50 and 130 degrees is 180 degrees. We can thus write the following equation:

$\dpi{100} measure\ of\ \angle A+ measure\ of\ supplement\ of\ \angle A=180$

$\dpi{100} 40-10x+ measure\ of\ supplement\ of\ \angle A=180$

Subtract 40 from both sides.

$\dpi{100} -10x+ measure\ of\ supplement\ of\ \angle A=140$

Add $\dpi{100} 10x$ to both sides.

$\dpi{100} measure\ of\ supplement\ of\ \angle A=140+10x=10x+140$

The answer is $(10x+140)^{\circ}$ .

Report an Error

Example Question #1 : Geometry

In the following diagram, lines and are parallel to each other. What is the value for ?

Sat_math_166_03

Possible Answers:

60^o

100^o

30^o

It cannot be determined

80^o

Correct answer:

80^o

Explanation:

When two parallel lines are intersected by another line, the sum of the measures of the interior angles on the same side of the line is 180°. Therefore, the sum of the angle that is labeled as 100° and angle y is 180°. As a result, angle y is 80°.

Another property of two parallel lines that are intersected by a third line is that the corresponding angles are congruent. So, the measurement of angle x is equal to the measurement of angle y, which is 80°.

Report an Error

Example Question #1 : How To Find An Angle

Lines

Examine the above diagram. If $l \parallel m$ , give in terms of .

Possible Answers:

75-x

165 +x

165-x

131 -x

75 + x

Correct answer:

165-x

Explanation:

The two marked angles are same-side exterior angles of parallel lines, which are supplementary - that is, their measures have sum 180. We can solve for in this equation:

(y-17) + (x + 32) = 180

y + x-17 + 32= 180

y + x+15= 180

y + x+15- 15 - x = 180- 15 - x

y = 165- x

Report an Error

Example Question #2 : How To Find An Angle

Lines

Examine the above diagram. If $l \parallel m$ , give in terms of .

Possible Answers:

$47 - \frac{1}{2}x$

92 - x

47 - x

$184 - \frac{1}{2}x$

$92 - \frac{1}{2}x$

Correct answer:

$92 - \frac{1}{2}x$

Explanation:

The two marked angles are same-side interior angles of parallel lines, which are supplementary - that is, their measures have sum 180. We can solve for in this equation:

(2y + 15) + (x - 19) = 180

2y + x+ 15 - 19 = 180

2y + x-4 = 180

2y + x-4+4 -x = 180+4 -x

2y = 184 -x

$2y \div 2 = \left ( 184 -x \right )\div 2$

$y= 92 - \frac{1}{2}x$

Report an Error

Example Question #3 : How To Find An Angle

Lines

Examine the above diagram. What is x + y ?

Possible Answers:

112

Correct answer:

Explanation:

By angle addition,

$\left ( x - 13\right )+ 100 + (y + 25) = 180$

$x - 13\right+ 100 + y + 25 = 180$

$x + y - 13\right+ 100+ 25 = 180$

x + y +112 = 180

x + y +112 - 112= 180- 112

x + y = 68

Report an Error

Example Question #251 : Geometry

Lines

Examine the above diagram. Which of the following statements must be true whether or not and are parallel?

Possible Answers:

$\angle 5 \cong \angle 4$

$\angle 2 \cong \angle 6$

$m \angle 4 + m \angle 7 = 180 ^{\circ }$

$m \angle 1 + m \angle 6 = 180 ^{\circ }$

$\angle 5 \cong \angle 8$

Correct answer:

$\angle 5 \cong \angle 8$

Explanation:

Four statements can be eliminated by the various parallel theorems and postulates. Congruence of alternate interior angles or corresponding angles forces the lines to be parallel, so

$\angle 5 \cong \angle 4 \Rightarrow l \parallel m$ and

$\angle 2 \cong \angle 6 \Rightarrow l \parallel m$ .

Also, if same-side interior angles or same-side exterior angles are supplementary, the lines are parallel, so

$m \angle 4 + m \angle 7 = 180 ^{\circ } \Rightarrow l \parallel m$ and

$m \angle 1 + m \angle 6 = 180 ^{\circ } \Rightarrow l \parallel m$ .

However, $\angle 5 \cong \angle 8$ whether or not $l \parallel m$ since they are vertical angles, which are always congruent.

Report an Error

Example Question #5 : How To Find An Angle

$\angle 1$ and $\angle 2$ are supplementary; $\angle 1$ and $\angle 3$ are complementary.

$m \angle 2 = 100 ^{\circ }$ .

What is $m \angle 3$ ?

Possible Answers:

$100^{\circ }$

$80^{\circ }$

$10^{\circ }$

$50^{\circ }$

Correct answer:

$10^{\circ }$

Explanation:

Supplementary angles and complementary angles have measures totaling $180^{\circ }$ and $90^{\circ }$ , respectively.

$m \angle 2 = 100 ^{\circ }$ , so its supplement $\angle 1$ has measure

$m \angle 1 = 180^{\circ } - m \angle 2 = 180^{\circ } - 100 ^{\circ } = 80^{\circ }$

$\angle 3$ , the complement of $\angle 1$ , has measure

$m \angle 3 = 90^{\circ } - m \angle 1 = 90^{\circ } - 80 ^{\circ } = 10^{\circ }$

Report an Error

View Tutors

Joseph
Certified Tutor

Old Dominion University, Bachelor of Science, Electrical Engineering. Western Governors University, Masters in Education, Mat...

View Tutors

Magdy
Certified Tutor

Cairo University, Egypt, Bachelor of Science, Electrical Engineering. New Mexico State University-Main Campus, Doctor of Phil...

View Tutors

Mike Bahaa
Certified Tutor

Concordia University-Ann Arbor, Master of Arts Teaching, Mathematics Teacher Education.

All HSPT Math Resources

6 Diagnostic Tests 130 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Physics Tutors in New York City, English Tutors in San Francisco-Bay Area, ACT Tutors in Washington DC, GMAT Tutors in Seattle, Spanish Tutors in San Diego, SSAT Tutors in Dallas Fort Worth, Spanish Tutors in Denver, Reading Tutors in Chicago, Reading Tutors in New York City, GMAT Tutors in Boston

Popular Courses & Classes

SSAT Courses & Classes in Boston, Spanish Courses & Classes in Houston, ACT Courses & Classes in Atlanta, GRE Courses & Classes in San Diego, SSAT Courses & Classes in Houston, GRE Courses & Classes in Houston, LSAT Courses & Classes in Los Angeles, MCAT Courses & Classes in San Diego, GRE Courses & Classes in New York City, LSAT Courses & Classes in Denver

Popular Test Prep

SAT Test Prep in Denver, LSAT Test Prep in San Diego, SSAT Test Prep in Phoenix, SSAT Test Prep in New York City, GRE Test Prep in New York City, MCAT Test Prep in San Francisco-Bay Area, GMAT Test Prep in Denver, SSAT Test Prep in San Francisco-Bay Area, SAT Test Prep in Philadelphia, SAT Test Prep in Miami

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

HSPT Math : Geometry

Study concepts, example questions & explanations for HSPT Math

All HSPT Math Resources

Example Questions

Example Question #781 : New Sat

Example Question #1 : Geometry

Example Question #1 : Geometry

Example Question #1 : Plane Geometry

Example Question #1 : Geometry

Example Question #1 : How To Find An Angle

Example Question #2 : How To Find An Angle

Example Question #3 : How To Find An Angle

Example Question #251 : Geometry

Example Question #5 : How To Find An Angle

All HSPT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: