We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

Basic Geometry : Plane Geometry

Study concepts, example questions & explanations for Basic Geometry

Create An Account

All Basic Geometry Resources

9 Diagnostic Tests 164 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #11 : How To Find If Right Triangles Are Congruent

Are these right triangles congruent?

Congruent right triangles

Possible Answers:

Yes - by the angle-angle-side theorem

Cannot be determined - we need at least one pair of angles, or all three sides

No - the angles are different

Yes - all three pairs of sides must be congruent by Pythagorean Theorem

No - at least one pair of corresponding sides is not congruent

Correct answer:

Yes - all three pairs of sides must be congruent by Pythagorean Theorem

Explanation:

Right now we can't directly compare these triangles because we do not know all three side lengths. However, we can use Pythagorean Theorem to determine both missing sides. The left triangle is missing the hypotenuse:

$\small 48^2 + 55^2 = c^2$

$\small 2,304 + 3,025 = c^2$

$\small 5,329 = c$

$\small c = \sqrt{5,329}= 73$

The right triangle is missing one of the legs:

$\small x^2 + 48^2 = 78^2$

$\small x^2 + 2,304 = 5,329$ subtract 2,304 from both sides

$\small x^2 = 3,025$

$\small x = \sqrt{3,025} = 55$

This means that the two triangles both have side lengths 48, 55, 73, so they must be congruent.

Report an Error

Example Question #1481 : Plane Geometry

The hypotenuse and acute angle are given for several triangles. Which if any are congruent? Triangle A- Hypotenuse=15; acute angle=56 degrees. Triangle B- Hypotenuse=18; acute angle=56 degrees. Triangle C-Hypotenuse=18; acute angle= 45 degrees.

Possible Answers:

All three.

A & B

None of these

A & C

B & C

Correct answer:

None of these

Explanation:

The correct answer is none of these. There are several pairs of angles and sides or sides and angles that must be the same in order for two triangles to be congruent.

In our case, we need the acute angle and the hypotenuse to both be equal. No two triangles above have this relationship and therefore no two are congruent.

Report an Error

Example Question #1483 : Basic Geometry

Given: $\bigtriangleup ABC$ and $\bigtriangleup DEF$ .

$\angle B$ and $\angle E$ are both right angles.

$\overline{AB } \cong \overline{DE}$

$\overline{AC} \cong \overline{DF}$

True or false: From the above information, it follows that $\bigtriangleup ABC \cong \bigtriangleup DEF$ .

Possible Answers:

True

False

Correct answer:

True

Explanation:

If we seek to prove that $\bigtriangleup ABC \cong \bigtriangleup DEF$ , then , , and correspond to , , and , respectively.

By the Hypotenuse-Leg Theorem (HL), if the hypotenuse and one leg of a triangle are congruent to those of another, the triangles are congruent.

$\angle B$ and $\angle E$ are both right angles, so $\bigtriangleup ABC$ and $\bigtriangleup DEF$ are both right triangles. $\overline{AB }$ and $\overline{DE}$ are congruent corresponding sides, and moreover, since, each includes the right-angle vertex as an endpoint, they are congruent corresponding legs. $\overline{AC}$ and $\overline{DF}$ are opposite the right angles, making them congruent corresponding hypotenuses.

The conditions of HL are satisfied, so $\bigtriangleup ABC \cong \bigtriangleup DEF$ .

Report an Error

Example Question #302 : Right Triangles

Given: $\bigtriangleup ABC$ and $\bigtriangleup DEF$ .

$\angle B$ and $\angle E$ are both right angles.

$\overline{AB} \cong \overline{BC}$

$\overline{DE} \cong \overline{EF}$

True or false: From the given information, it follows that $\bigtriangleup ABC \cong \bigtriangleup DEF$ .

Possible Answers:

False

True

Correct answer:

False

Explanation:

The congruence of $\bigtriangleup ABC$ and $\bigtriangleup DEF$ cannot be proved from the given information alone. Examine the two triangles below:

Triangles 2

$\overline{AB} \cong \overline{BC}$ , $\overline{DE} \cong \overline{EF}$ , and $\angle B$ and $\angle E$ are both right angles, so the conditions of the problem are met; however, since the sides are not congruent between triangles - for example, $\overline{AB} \ncong \overline{DE}$ - the triangles are not congruent either.

Report an Error

Example Question #1 : How To Find The Height Of A Right Triangle

A right triangle has a hypotenuse of 18 inches and a base of 12 inches. What is the height of the triangle in inches?

Possible Answers:

13.42

8.73

180.2

12.55

Correct answer:

13.42

Explanation:

We can find one leg of a right triangle when we have the length of the hypotenuse and the other leg. Square the hypotenuse and the known leg. Then, subtract the squared length of the leg from the squared length of the hypotenuse. Finally, find the square root of the result.

$\sqrt{18^{2}-12^{2}}=13.42$

Report an Error

Example Question #1 : How To Find The Height Of A Right Triangle

Screen_shot_2015-02-27_at_6.56.15_pm

If c is not the base of the triangle, which of the following is the height?

Possible Answers:

None of the other answers

Correct answer:

Explanation:

If is not the base, that makes either or the base. If either or is the base, the right angle is on the bottom, so or respectively will be perpendicular. The height of a triangle is the distance from the base to the highest point, and in a right triangle that will be found by the side adjoining the base at a right angle. So if the base is , then and vise versa.

Report an Error

Example Question #1482 : Plane Geometry

The area of a right triangle is 28. If one leg has a length of 7, what is the length of the other leg?

Possible Answers:

Correct answer:

Explanation:

We begin with the formula for the area of a triangle.

$A=\frac{1}{2}bh$

We further realize that the two legs of the triangle are the base and height; therefore, substituting what we know we get

$28=\frac{1}{2}(7)h$

$28=\frac{7}{2}h$

We can then solve by simply dividing.

8 = h

We have found our height and thus the second leg of our triangle.

Report an Error

Example Question #311 : Right Triangles

If the area of a right triangle is , and the base of the right triangle is , what is the height of the right triangle?

Possible Answers:

Correct answer:

Explanation:

Recall how to find the area of a right triangle:

$\text{Area}=\frac{1}{2}(\text{base}\times\text{height})$

Now, we are going to manipulate the equation to solve for height.

$2(\text{Area})=\text{base}\times\text{height}$

$\text{Height}=\frac{2(\text{Area})}{\text{base}}$

Now, plug in the information given by the question about the values of the area and base of the triangle to find the height.

$\text{Height}=\frac{2(16)}{4}=\frac{32}{4}=8$

Report an Error

Example Question #1 : How To Find The Height Of A Right Triangle

If the area of a right triangle is , and the base of the triangle is , what is the height of the triangle?

Possible Answers:

Correct answer:

Explanation:

Recall how to find the area of a right triangle:

$\text{Area}=\frac{1}{2}(\text{base}\times\text{height})$

Now, we are going to manipulate the equation to solve for height.

$2(\text{Area})=\text{base}\times\text{height}$

$\text{Height}=\frac{2(\text{Area})}{\text{base}}$

Now, plug in the information given by the question about the values of the area and base of the triangle to find the height.

$\text{Height}=\frac{2(10)}{5}=\frac{20}{5}=4$

Report an Error

Example Question #2 : How To Find The Height Of A Right Triangle

If the area of a right triangle is , and the base of the triangle is , what is the height of the triangle?

Possible Answers:

1.5

4.5

Correct answer:

Explanation:

Recall how to find the area of a right triangle:

$\text{Area}=\frac{1}{2}(\text{base}\times\text{height})$

Now, we are going to manipulate the equation to solve for height.

$2(\text{Area})=\text{base}\times\text{height}$

$\text{Height}=\frac{2(\text{Area})}{\text{base}}$

Now, plug in the information given by the question about the values of the area and base of the triangle to find the height.

$\text{Height}=\frac{2(15)}{10}=\frac{30}{10}=3$

Report an Error

View Tutors

Charone
Certified Tutor

Troy University, Bachelor of Science, Education.

View Tutors

William
Certified Tutor

University of Virginia-Main Campus, Bachelor in Arts, English. Shenandoah University, Master of Science, Education.

View Tutors

James
Certified Tutor

University of Georgia, Bachelor in Arts, Political Science and Government.

All Basic Geometry Resources

9 Diagnostic Tests 164 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Biology Tutors in New York City, Computer Science Tutors in San Diego, Reading Tutors in Atlanta, SSAT Tutors in Atlanta, French Tutors in Denver, MCAT Tutors in Chicago, Physics Tutors in Seattle, Biology Tutors in Los Angeles, English Tutors in Seattle, Chemistry Tutors in Seattle

Popular Courses & Classes

GRE Courses & Classes in New York City, GMAT Courses & Classes in Chicago, GMAT Courses & Classes in Atlanta, ISEE Courses & Classes in Los Angeles, SSAT Courses & Classes in Phoenix, GRE Courses & Classes in Seattle, LSAT Courses & Classes in New York City, GRE Courses & Classes in Houston, ACT Courses & Classes in Seattle, SAT Courses & Classes in Chicago

Popular Test Prep

MCAT Test Prep in Los Angeles, GRE Test Prep in Houston, GMAT Test Prep in Washington DC, SAT Test Prep in San Francisco-Bay Area, MCAT Test Prep in Phoenix, SAT Test Prep in Boston, SSAT Test Prep in Atlanta, SSAT Test Prep in Seattle, SSAT Test Prep in Houston, SSAT Test Prep in San Francisco-Bay Area

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

Basic Geometry : Plane Geometry

Study concepts, example questions & explanations for Basic Geometry

All Basic Geometry Resources

Example Questions

Example Question #11 : How To Find If Right Triangles Are Congruent

Example Question #1481 : Plane Geometry

Example Question #1483 : Basic Geometry

Example Question #302 : Right Triangles

Example Question #1 : How To Find The Height Of A Right Triangle

Example Question #1 : How To Find The Height Of A Right Triangle

Example Question #1482 : Plane Geometry

Example Question #311 : Right Triangles

Example Question #1 : How To Find The Height Of A Right Triangle

Example Question #2 : How To Find The Height Of A Right Triangle

All Basic Geometry Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: