Call Now to Set Up Tutoring:

(888) 888-0446

Common Core: High School - Geometry : Prove Parallelogram Theorems: CCSS.Math.Content.HSG-CO.C.11

Study concepts, example questions & explanations for Common Core: High School - Geometry

Create An Account

All Common Core: High School - Geometry Resources

6 Diagnostic Tests 114 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #9 : Parallelogram Proofs

True or False: Is the following quadrilateral a parallelogram?

Screen shot 2020 08 20 at 8.35.53 am

Possible Answers:

False

True

Correct answer:

True

Explanation:

This is true because a theorem states that if a quadrilateral has two consecutive angles that are supplementary, then the quadrilateral is a parallelogram.

Report an Error

Example Question #501 : High School: Geometry

Prove that if the following quadrilateral has a pair of opposite parallel, congruent sides, it is a parallelogram.

Screen shot 2020 08 20 at 9.22.22 am

Possible Answers:

Proof:

Screen shot 2020 08 20 at 9.24.06 am

Proof:

Screen shot 2020 08 20 at 9.24.46 am

Proof:

Screen shot 2020 08 20 at 9.23.33 am

Correct answer:

Proof:

Screen shot 2020 08 20 at 9.24.46 am

Explanation:

Thus, we have shown that if a quadrilateral has one pair of parallel, congruent opposite sides, then it is a parallelogram.

Screen shot 2020 08 20 at 9.22.33 am

Report an Error

Example Question #21 : Prove Parallelogram Theorems: Ccss.Math.Content.Hsg Co.C.11

Prove that since this quadrilateral has two pairs of opposite congruent angles it is a parallelogram.

Screen shot 2020 08 20 at 9.48.56 am

Possible Answers:

Proof:

Screen shot 2020 08 20 at 9.50.51 am

Proof:

Screen shot 2020 08 20 at 9.51.28 am

Proof:

Screen shot 2020 08 20 at 9.50.12 am

Correct answer:

Proof:

Screen shot 2020 08 20 at 9.50.51 am

Explanation:

Screen shot 2020 08 20 at 9.49.06 am

Thus, we have shown that if a quadrilateral has two pairs of opposite congruent angles, it is a parallelogram.

Report an Error

Example Question #151 : Congruence

Prove the following parallelogram has two pairs of opposite congruent angles.

Screen shot 2020 08 20 at 10.02.30 am

Possible Answers:

Proof:

ABCD is a parallelogram (given)

We can add the line across the diagonal

Screen shot 2020 08 20 at 10.04.42 am

$\overline{AB}$ is parallel to $\overline{CD}$

$\overline{AC}$ is parallel to $\overline{BD}$ (definition of a parallelogram)

$\angle 1\cong \angle 4$

$\angle 2\cong \angle 3$ (alternate interior angles)

$\overline{CB}$ is a common side between $\Delta ABC$ and $\Delta DCB$

$\Delta ABC\cong \Delta DCB$ (By Angle-Side-Angle Theorem)

$\angle A\cong \angle D$ (corresponding parts of congruent triangles)

$\angle 1= \angle 4, \angle 2= \angle 3$

$\angle 1+\angle 2= \angle 4+\angle 3$ (Addition of equalities)

$\angle 1+\angle 2= \angle C$

$\angle 4+\angle 3= \angle B$ (Angle Addition Postulate)

$\angle C= \angle B$

$\angle C\cong \angle B$

Therefore $\angle A\cong \angle D$ and $\angle C\cong \angle B$

Proof:

ABCD is a parallelogram (given)

We can add the line across the diagonal

Screen shot 2020 08 20 at 10.04.42 am

$\overline{AB}$ is parallel to $\overline{CD}$

$\overline{AC}$ is parallel to $\overline{BD}$ (definition of a parallelogram)

$\angle 1\cong \angle 4$

$\angle 2\cong \angle 3$ (alternate interior angles)

$\overline{CB}$ is a common side between $\Delta ABC$ and $\Delta DCB$

$\Delta ABC\cong \Delta DCB$ (By Angle-Side-Angle Theorem)

Because the triangles are congruent we can assume:

$\angle C\cong \angle B$ , $\angle A\cong \angle D$

Therefore $\angle A\cong \angle D$ and $\angle C\cong \angle B$

Proof:

ABCD is a parallelogram (given)

We can add the line across the diagonal

Screen shot 2020 08 20 at 10.04.42 am

$\overline{AB}$ is parallel to $\overline{CD}$

$\overline{AC}$ is parallel to $\overline{BD}$ (definition of a parallelogram)

$\angle 1\cong \angle 4$

$\angle 2\cong \angle 3$ (corresponding angles)

$\overline{CB}$ is a common side between $\Delta ABC$ and $\Delta DCB$

$\Delta ABC\cong \Delta DCB$ (By Angle-Side-Angle Theorem)

$\angle A\cong \angle D$ (corresponding parts of congruent triangles)

$\angle 1= \angle 4, \angle 2= \angle 3$

$\angle 1+\angle 2= \angle 4+\angle 3$ (Addition of equalities)

$\angle 1+\angle 2= \angle C$

$\angle 4+\angle 3= \angle B$ (Angle Addition Postulate)

$\angle C= \angle B$

$\angle C\cong \angle B$

Therefore $\angle A\cong \angle D$ and $\angle C\cong \angle B$

Correct answer:

Proof:

ABCD is a parallelogram (given)

We can add the line across the diagonal

Screen shot 2020 08 20 at 10.04.42 am

$\overline{AB}$ is parallel to $\overline{CD}$

$\overline{AC}$ is parallel to $\overline{BD}$ (definition of a parallelogram)

$\angle 1\cong \angle 4$

$\angle 2\cong \angle 3$ (alternate interior angles)

$\overline{CB}$ is a common side between $\Delta ABC$ and $\Delta DCB$

$\Delta ABC\cong \Delta DCB$ (By Angle-Side-Angle Theorem)

$\angle A\cong \angle D$ (corresponding parts of congruent triangles)

$\angle 1= \angle 4, \angle 2= \angle 3$

$\angle 1+\angle 2= \angle 4+\angle 3$ (Addition of equalities)

$\angle 1+\angle 2= \angle C$

$\angle 4+\angle 3= \angle B$ (Angle Addition Postulate)

$\angle C= \angle B$

$\angle C\cong \angle B$

Therefore $\angle A\cong \angle D$ and $\angle C\cong \angle B$

Explanation:

Statement Reasoning

ABDC is a parallelogram. This is given in the problem.

We can add the line across the diagonal Connecting any two points make a line, so this is a valid line we can add.

Screen shot 2020 08 20 at 10.03.17 am

$\overline{AB}$ is parallel to $\overline{CD}$

$\overline{AC}$ is parallel to $\overline{BD}$ We know this to be true according to the definition of a parallelogram.

$\angle 1\cong \angle 4$

$\angle 2\cong \angle 3$ Line is a transversal line intersection two parallel lines. We could extend lines and or lines and to make this relationship more clear. Alternate interior angles are formed by this transversal line.

Screen shot 2020 08 20 at 10.03.56 am

$\overline{CB}$ is a common side between $\Delta ABC$ and $\Delta DCB$

$\Delta ABC\cong \Delta DCB$ We are able to use the Angle-Side-Angle Theorem because we have one congruent side between these two triangles, , and two pairs of congruent angles, $\angle 1\cong \angle 4$ , $\angle 2\cong \angle 3$

$\angle A\cong \angle D$ Congruent triangles have congruent corresponding parts by definition

$\angle 1= \angle 4, \angle 2= \angle 3$ Because these angles are congruent they are also equal

$\angle 1+\angle 2= \angle 4+\angle 3$ Since $\angle 2= \angle 3$ we can add one of these angles to each side and still keep the equation balanced and equal

$\angle 1+\angle 2= \angle C$

$\angle 4+\angle 3= \angle B$ The Angle Addition Postulate says that two side by side angles create a new angle whose measure is equal to their sum

$\angle C= \angle B$ We are simply substituting these equalities into the equation $\angle 1+\angle 2= \angle 4+\angle 3$

$\angle C\cong \angle B$ Equal angles are congruent

Therefore $\angle A\cong \angle D$ and $\angle C\cong \angle B$

Thus, we have proven that this parallelogram has two pairs of opposite congruent angles.

Report an Error

Example Question #21 : Prove Parallelogram Theorems: Ccss.Math.Content.Hsg Co.C.11

Prove the following parallelogram has diagonals that bisect each other.

Screen shot 2020 08 20 at 10.34.27 am

Possible Answers:

Proof:

Screen shot 2020 08 20 at 10.35.58 am

Proof:

Screen shot 2020 08 20 at 10.36.23 am

Proof:

Screen shot 2020 08 20 at 10.35.33 am

Correct answer:

Proof:

Screen shot 2020 08 20 at 10.35.58 am

Explanation:

Screen shot 2020 08 20 at 10.34.58 am

Report an Error

View Tutors

Sharif
Certified Tutor

NCCU, Bachelors, Physics and Mathematics.

View Tutors

Alejandro
Certified Tutor

Kennesaw State University, Bachelor of Science, Computer Software Engineering.

View Tutors

Joy
Certified Tutor

Boston University, Bachelor in Arts, Conservation Biology.

All Common Core: High School - Geometry Resources

6 Diagnostic Tests 114 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Spanish Tutors in Washington DC, LSAT Tutors in Phoenix, Physics Tutors in New York City, Calculus Tutors in Boston, GRE Tutors in San Francisco-Bay Area, Calculus Tutors in Dallas Fort Worth, Spanish Tutors in Phoenix, English Tutors in San Francisco-Bay Area, Math Tutors in Philadelphia, Statistics Tutors in New York City

Popular Courses & Classes

SSAT Courses & Classes in Philadelphia, MCAT Courses & Classes in Boston, LSAT Courses & Classes in San Francisco-Bay Area, MCAT Courses & Classes in Los Angeles, SSAT Courses & Classes in San Francisco-Bay Area, Spanish Courses & Classes in Denver, GMAT Courses & Classes in Washington DC, SAT Courses & Classes in Seattle, SSAT Courses & Classes in Washington DC, ISEE Courses & Classes in Miami

Popular Test Prep

SAT Test Prep in Houston, LSAT Test Prep in Washington DC, ISEE Test Prep in Los Angeles, LSAT Test Prep in Chicago, ISEE Test Prep in New York City, ACT Test Prep in Dallas Fort Worth, GRE Test Prep in Los Angeles, GMAT Test Prep in Chicago, GMAT Test Prep in Seattle, SSAT Test Prep in Washington DC

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

Common Core: High School - Geometry : Prove Parallelogram Theorems: CCSS.Math.Content.HSG-CO.C.11

Study concepts, example questions & explanations for Common Core: High School - Geometry

All Common Core: High School - Geometry Resources

Example Questions

Example Question #9 : Parallelogram Proofs

Example Question #501 : High School: Geometry

Example Question #21 : Prove Parallelogram Theorems: Ccss.Math.Content.Hsg Co.C.11

Example Question #151 : Congruence

Example Question #21 : Prove Parallelogram Theorems: Ccss.Math.Content.Hsg Co.C.11

All Common Core: High School - Geometry Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: