In the figure below, given that 𝐴𝐵𝐶𝐷 is a rectangle, 𝑂𝐵𝐶𝐻 is a parallelogram, and 𝐴𝑂 equals 3.7 centimetres, find the length of 𝐻𝐴.
Let’s start by adding in the information that 𝐴𝑂 is 3.7 centimetres. We can then also establish that the length 𝐻𝐴 is the line coloured in orange. Let’s see if we can use any of the facts we know about parallelograms or rectangles to help us work out this missing length.
We can recall that the opposite sides of a parallelogram are parallel and congruent, where congruent means the same length. This means that our line segment 𝐵𝐶, which is 11.8 centimetres, is parallel to our line segment 𝑂𝐻. And since it’s congruent, this means that 𝑂𝐻 is 11.8 centimetres.
So to find our line segment 𝐻𝐴, we can take the longer line segment of 𝑂𝐻 and subtract the line segment 𝐴𝑂. Therefore, 𝐻𝐴 is equal to 11.8 subtract 3.7, giving us 8.1 centimetres for the length of line segment 𝐻𝐴.