Question Video: Identifying the Triangle with the Same Area as a Given Triangle Using the Relations between Triangles Sharing the Same Base and between Parallel Lines Mathematics • Second Year of Preparatory School

Video Transcript

Which triangle has the same area as triangle 𝐿𝐵𝐶?

So here is triangle 𝐿𝐵𝐶. It would be triangle 𝐷𝑋𝐿 and not just because it looks like it. Here’s the reasons why. They share the same vertex at 𝐿. And they have equal base lengths and we know that because of these markings. But it’s important to add that the equal base lengths must lie along the same line. This is because if they’re on the same line and they meet at the same vertex, then their heights must be equal.

And this is important because the area of a triangle is equal to one-half times the base times the height. And if they have equal bases and equal heights, their areas must be exactly the same.

So once again, the triangle that has the same area as triangle 𝐿𝐵𝐶 would be triangle 𝐷𝑋𝐿.