{"appState":{"pageLoadApiCallsStatus":true},"articleState":{"article":{"headers":{"creationTime":"2016-03-26T07:10:07+00:00","modifiedTime":"2016-03-26T07:10:07+00:00","timestamp":"2022-09-14T17:46:02+00:00"},"data":{"breadcrumbs":[{"name":"Academics & The Arts","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33662"},"slug":"academics-the-arts","categoryId":33662},{"name":"Math","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33720"},"slug":"math","categoryId":33720},{"name":"Geometry","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33725"},"slug":"geometry","categoryId":33725}],"title":"Properties of Parallelograms — Practice Geometry Questions","strippedTitle":"properties of parallelograms — practice geometry questions","slug":"properties-of-parallelograms-practice-geometry-questions","canonicalUrl":"","seo":{"metaDescription":"In two-dimensional geometry, a parallelogram is a quadrilateral (a four-sided figure) with two pairs of congruent sides and two pairs of congruent angles. The f","noIndex":0,"noFollow":0},"content":"In two-dimensional geometry, a parallelogram is a quadrilateral (a four-sided figure) with two pairs of congruent sides and two pairs of congruent angles. The following practice questions ask you to use the properties of parallelograms to find missing angles and variables.\n<h2 id=\"tab1\" >Practice questions</h2>\n<img src=\"https://www.dummies.com/wp-content/uploads/501529.image0.png\" height=\"129\" alt=\"image0.png\" width=\"250\"/>\nIn parallelogram MATH, diagonals \n<img src=\"https://www.dummies.com/wp-content/uploads/501530.image1.png\" height=\"21\" alt=\"image1.png\" width=\"81\"/>\nintersect at E. Use the figure and the given information to solve the following questions.\n<ol class=\"level-one\">\n <li>If AT = 2a + 3b, MH = 28, AM = 4a + b, and TH = 26, find the sum of a + b.\n </li>\n <li>If \n<img src=\"https://www.dummies.com/wp-content/uploads/501531.image2.png\" height=\"19\" alt=\"image2.png\" width=\"275\"/>\nfind the degree measure of \n<img src=\"https://www.dummies.com/wp-content/uploads/501532.image3.png\" height=\"16\" alt=\"image3.png\" width=\"53\"/>\n </li>\n</ol>\n<h2 id=\"tab2\" >Answers and explanations</h2>\n<ol class=\"level-one\">\n <li>11\nOpposite sides of a parallelogram are congruent. Therefore, AM = TH and AT = MH. Solve 4a + b = 26 for b:\n<img src=\"https://www.dummies.com/wp-content/uploads/501533.image4.png\" height=\"40\" alt=\"image4.png\" width=\"104\"/>\nNow plug the value of b into 2a + 3b = 28 and solve for a:\n<img src=\"https://www.dummies.com/wp-content/uploads/501534.image5.png\" height=\"128\" alt=\"image5.png\" width=\"140\"/>\nPlug in the value of a to find b:\n<img src=\"https://www.dummies.com/wp-content/uploads/501535.image6.png\" height=\"27\" alt=\"image6.png\" width=\"171\"/>\nTherefore, a + b = 5 + 6 = 11.\n </li>\n <li>79 degrees\n<img src=\"https://www.dummies.com/wp-content/uploads/501536.image7.png\" height=\"175\" alt=\"image7.png\" width=\"300\"/>\nYou know that\n<img src=\"https://www.dummies.com/wp-content/uploads/501537.image8.png\" height=\"16\" alt=\"image8.png\" width=\"120\"/>\nare vertical angles. Vertical angles are congruent, so\n<img src=\"https://www.dummies.com/wp-content/uploads/501538.image9.png\" height=\"80\" alt=\"image9.png\" width=\"127\"/>\nTherefore, \n<img src=\"https://www.dummies.com/wp-content/uploads/501539.image10.png\" height=\"27\" alt=\"image10.png\" width=\"369\"/>\nare supplementary angles, which means they add up to 180 degrees:\n<img src=\"https://www.dummies.com/wp-content/uploads/501540.image11.png\" height=\"59\" alt=\"image11.png\" width=\"173\"/>\n </li>\n</ol>","description":"In two-dimensional geometry, a parallelogram is a quadrilateral (a four-sided figure) with two pairs of congruent sides and two pairs of congruent angles. The following practice questions ask you to use the properties of parallelograms to find missing angles and variables.\n<h2 id=\"tab1\" >Practice questions</h2>\n<img src=\"https://www.dummies.com/wp-content/uploads/501529.image0.png\" height=\"129\" alt=\"image0.png\" width=\"250\"/>\nIn parallelogram MATH, diagonals \n<img src=\"https://www.dummies.com/wp-content/uploads/501530.image1.png\" height=\"21\" alt=\"image1.png\" width=\"81\"/>\nintersect at E. Use the figure and the given information to solve the following questions.\n<ol class=\"level-one\">\n <li>If AT = 2a + 3b, MH = 28, AM = 4a + b, and TH = 26, find the sum of a + b.\n </li>\n <li>If \n<img src=\"https://www.dummies.com/wp-content/uploads/501531.image2.png\" height=\"19\" alt=\"image2.png\" width=\"275\"/>\nfind the degree measure of \n<img src=\"https://www.dummies.com/wp-content/uploads/501532.image3.png\" height=\"16\" alt=\"image3.png\" width=\"53\"/>\n </li>\n</ol>\n<h2 id=\"tab2\" >Answers and explanations</h2>\n<ol class=\"level-one\">\n <li>11\nOpposite sides of a parallelogram are congruent. Therefore, AM = TH and AT = MH. Solve 4a + b = 26 for b:\n<img src=\"https://www.dummies.com/wp-content/uploads/501533.image4.png\" height=\"40\" alt=\"image4.png\" width=\"104\"/>\nNow plug the value of b into 2a + 3b = 28 and solve for a:\n<img src=\"https://www.dummies.com/wp-content/uploads/501534.image5.png\" height=\"128\" alt=\"image5.png\" width=\"140\"/>\nPlug in the value of a to find b:\n<img src=\"https://www.dummies.com/wp-content/uploads/501535.image6.png\" height=\"27\" alt=\"image6.png\" width=\"171\"/>\nTherefore, a + b = 5 + 6 = 11.\n </li>\n <li>79 degrees\n<img src=\"https://www.dummies.com/wp-content/uploads/501536.image7.png\" height=\"175\" alt=\"image7.png\" width=\"300\"/>\nYou know that\n<img src=\"https://www.dummies.com/wp-content/uploads/501537.image8.png\" height=\"16\" alt=\"image8.png\" width=\"120\"/>\nare vertical angles. Vertical angles are congruent, so\n<img src=\"https://www.dummies.com/wp-content/uploads/501538.image9.png\" height=\"80\" alt=\"image9.png\" width=\"127\"/>\nTherefore, \n<img src=\"https://www.dummies.com/wp-content/uploads/501539.image10.png\" height=\"27\" alt=\"image10.png\" width=\"369\"/>\nare supplementary angles, which means they add up to 180 degrees:\n<img src=\"https://www.dummies.com/wp-content/uploads/501540.image11.png\" height=\"59\" alt=\"image11.png\" width=\"173\"/>\n </li>\n</ol>","blurb":"","authors":[{"authorId":8986,"name":"Allen Ma","slug":"allen-ma","description":" Allen Ma and Amber Kuang are math teachers at John F. Kennedy High School in Bellmore, NY. Allen has taught geometry for more than 25 years, has coached the math team, and is a former honors math research coordinator. Amber has taught all levels of math, from algebra to calculus, for 20 years. ","hasArticle":false,"_links":{"self":"https://dummies-api.dummies.com/v2/authors/8986"}},{"authorId":8987,"name":"Amber Kuang","slug":"amber-kuang","description":" Allen Ma and Amber Kuang are math teachers at John F. Kennedy High School in Bellmore, NY. Allen has taught geometry for more than 25 years, has coached the math team, and is a former honors math research coordinator. Amber has taught all levels of math, from algebra to calculus, for 20 years. 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Properties of Parallelograms — Practice Geometry Questions

By: Allen Ma and Amber Kuang and

Updated: 03-26-2016

From The Book: Geometry: 1,001 Practice Problems For Dummies (+ Free Online Practice)

Geometry: 1,001 Practice Problems For Dummies (+ Free Online Practice)

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In two-dimensional geometry, a parallelogram is a quadrilateral (a four-sided figure) with two pairs of congruent sides and two pairs of congruent angles. The following practice questions ask you to use the properties of parallelograms to find missing angles and variables.

Practice questions

In parallelogram MATH, diagonals

intersect at E. Use the figure and the given information to solve the following questions.

If AT = 2a + 3b, MH = 28, AM = 4a + b, and TH = 26, find the sum of a + b.
If

find the degree measure of

Answers and explanations

11

Opposite sides of a parallelogram are congruent. Therefore, AM = TH and AT = MH. Solve 4a + b = 26 for b:

Now plug the value of b into 2a + 3b = 28 and solve for a:

Plug in the value of a to find b:

Therefore, a + b = 5 + 6 = 11.
79 degrees

You know that

are vertical angles. Vertical angles are congruent, so

Therefore,

are supplementary angles, which means they add up to 180 degrees:

About This Article

This article is from the book:

Geometry: 1,001 Practice Problems For Dummies (+ Free Online Practice) ,

About the book authors:

Allen Ma and Amber Kuang are math teachers at John F. Kennedy High School in Bellmore, New York. Allen, who has taught geometry for 20 years, is the math team coach and a former honors math research coordinator. Amber has taught all levels of mathematics, from algebra to calculus, for the past 14 years.

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Geometry ,

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