Question Video: Finding the Length of a Side in a Triangle given the Corresponding Side in a Congruent Triangle | Nagwa Question Video: Finding the Length of a Side in a Triangle given the Corresponding Side in a Congruent Triangle | Nagwa

# Question Video: Finding the Length of a Side in a Triangle given the Corresponding Side in a Congruent Triangle Mathematics

Find the length of line segment πΈπΆ.

02:57

### Video Transcript

Find the length of line segment πΈπΆ.

Before we start looking at the length of πΈπΆ, letβ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 π·π΄π΅πΆ, we can see that there are two parallel sides and two 90-degree angles. So the angle π·π΄π΅ and the angle π·πΆπ΅ must also be 90 degrees, as we would have pairs of supplementary angles. We can conclude, therefore, that our shape π·π΄πΆπ΅ is a rectangle. We have been asked to find the length of line segment πΈπΆ. But so far, using the fact that π·π΄πΆπ΅ is a rectangle isnβt enough information to help us with this. Letβs then have a look at the other shapes in this diagram.

We have a triangle πΉπ·π΄ and a triangle πΉπΆπΈ. Letβs start by looking at our side length π·πΉ in our purple Triangle and our side length πΉπΆ in our orange triangle. We can see from our diagram that these two lengths are congruent. That is, line segment π·πΉ is equal to the line segment πΉπΆ. We can see that the measure of angle πΉπ·π΄ is 90 degrees. And if we look at the angle πΉπΆπΈ in triangle πΉπΆπΈ, 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 πΉπΆπΈ is 90 degrees and giving us that we have two equivalent angles in our triangles.

Next, if we have a look at the angle π·πΉπ΄ in triangle πΉπ·π΄, then we can say that it must be equal to the measure of angle πΈπΉπΆ in triangle πΉπΆπΈ. Since these are opposite angles. So if we look at the information weβ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 πΉπ·π΄ and πΉπΆπΈ are congruent using the angle side angle congruency criterion.

Letβs see if this helps us workout the length of line segment πΈπΆ. We can establish since our triangles are congruent, then our length πΈπΆ in triangle πΉπΆπΈ is congruent to our length π·π΄ in triangle πΉπ·π΄. But what is the length of π·π΄? Well, if we return to the fact that our shape π·π΄πΆπ΅ is a rectangle, we know that opposite sides are equal in length. So the length of π·π΄ must be equal to the length of πΆπ΅, which is 7.5 centimetres. And so we conclude that because π·π΄ is equal to 7.5 centimetres, then the length of our line segment πΈπΆ is also 7.5 centimetres.

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