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.

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

  2. If


    find the degree measure of


Answers and explanations

  1. 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.

  2. 79 degrees


    You know that


    are vertical angles. Vertical angles are congruent, so




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


About This Article

This article is from the book:

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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