Question Video: Finding the Length of a Side in a Triangle given the Corresponding Side in a Congruent Triangle Mathematics • 8th Grade

Find the length of line segment 𝐸𝐢.


Video Transcript

Find the length of line segment 𝐸𝐢.

Before we start looking at the length of 𝐸𝐢, let’s have a look at our diagram and see if we can work out any of the shapes in it. If we look at our shape 𝐷𝐴𝐡𝐢, we can see that there are two parallel sides and two 90-degree angles. So the angle 𝐷𝐴𝐡 and the angle 𝐷𝐢𝐡 must also be 90 degrees, as we would have pairs of supplementary angles. We can conclude, therefore, that our shape 𝐷𝐴𝐢𝐡 is a rectangle. We have been asked to find the length of line segment 𝐸𝐢. But so far, using the fact that 𝐷𝐴𝐢𝐡 is a rectangle isn’t enough information to help us with this. Let’s then have a look at the other shapes in this diagram.

We have a triangle 𝐹𝐷𝐴 and a triangle 𝐹𝐢𝐸. Let’s start by looking at our side length 𝐷𝐹 in our purple Triangle and our side length 𝐹𝐢 in our orange triangle. We can see from our diagram that these two lengths are congruent. That is, line segment 𝐷𝐹 is equal to the line segment 𝐹𝐢. We can see that the measure of angle 𝐹𝐷𝐴 is 90 degrees. And if we look at the angle 𝐹𝐢𝐸 in triangle 𝐹𝐢𝐸, then we can note that this must be 90 degrees since we have a straight line with one 90-degree angle on it. So we can say that the measure of angle 𝐹𝐢𝐸 is 90 degrees and giving us that we have two equivalent angles in our triangles.

Next, if we have a look at the angle 𝐷𝐹𝐴 in triangle 𝐹𝐷𝐴, then we can say that it must be equal to the measure of angle 𝐸𝐹𝐢 in triangle 𝐹𝐢𝐸. Since these are opposite angles. So if we look at the information we’ve just recorded, we can see that we have an equivalent angle and equivalent side and another equivalent angle. This means that we can say that our triangles 𝐹𝐷𝐴 and 𝐹𝐢𝐸 are congruent using the angle side angle congruency criterion.

Let’s see if this helps us workout the length of line segment 𝐸𝐢. We can establish since our triangles are congruent, then our length 𝐸𝐢 in triangle 𝐹𝐢𝐸 is congruent to our length 𝐷𝐴 in triangle 𝐹𝐷𝐴. But what is the length of 𝐷𝐴? Well, if we return to the fact that our shape 𝐷𝐴𝐢𝐡 is a rectangle, we know that opposite sides are equal in length. So the length of 𝐷𝐴 must be equal to the length of 𝐢𝐡, which is 7.5 centimetres. And so we conclude that because 𝐷𝐴 is equal to 7.5 centimetres, then the length of our line segment 𝐸𝐢 is also 7.5 centimetres.

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.