Properties of Parallelograms — Practice Geometry Questions - dummies

Properties of Parallelograms — Practice Geometry Questions

By Allen Ma, Amber Kuang

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

image0.png

In parallelogram MATH, diagonals

image1.png

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

    image2.png

    find the degree measure of

    image3.png

Answers and explanations

  1. 11

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

    image4.png

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

    image5.png

    Plug in the value of a to find b:

    image6.png

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

  2. 79 degrees

    image7.png

    You know that

    image8.png

    are vertical angles. Vertical angles are congruent, so

    image9.png

    Therefore,

    image10.png

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

    image11.png