Parallelograms are one of the most important shapes in geometry. They are used extensively in various fields, including architecture, engineering, and design. Understanding the properties of parallelograms is crucial for solving problems related to these fields. In this article, we will discuss the properties of parallelograms and provide practice problems with an answer key.
Properties of Parallelograms
Parallelograms have several unique properties that set them apart from other shapes. One of the most important properties is that opposite sides are parallel. This means that if we draw a line connecting two opposite corners of a parallelogram, that line will be parallel to the opposite side of the parallelogram. Another important property of parallelograms is that opposite sides are equal in length. This means that if we measure the length of one side of a parallelogram, we can use that measurement to find the length of the opposite side.
Practice Problem 1:
Find the length of the missing side of the parallelogram given below.
Since opposite sides of a parallelogram are equal in length, we can find the missing side by subtracting the length of the known side from the perimeter of the parallelogram and dividing the result by 2.
Perimeter = 11 + 8 + 11 = 30
Length of missing side = (30 - 8 - 11) / 2 = 5.5
Therefore, the length of the missing side is 5.5.
Practice Problem 2:
Find the value of x in the parallelogram given below.
Since opposite sides of a parallelogram are parallel, we can use the fact that alternate angles are equal to find the value of x.
Alternate angles are angles that are on opposite sides of a transversal and on different parallel lines. In the parallelogram above, angle A is an alternate angle to angle C, and angle B is an alternate angle to angle D.
Since angle C is equal to 120 degrees, angle A is also equal to 120 degrees.
Angle A + x = 180 degrees (because the sum of angles in a triangle is 180 degrees)
120 + x = 180
x = 60 degrees
Therefore, the value of x is 60 degrees.
Parallelograms are an important shape in geometry, and understanding their properties is crucial for solving problems related to various fields. We hope this article has provided you with a better understanding of the properties of parallelograms and has helped you practice solving problems related to them. Remember to always check your answers using the answer key provided.