Roofs are angled downwards (i think that's what you mean, because if you look at most roofs straight on, they're rectangles...) in order to let rain flow downward into the drainage gutters. this helps slow down wear and tear

OK, so as jehan sez, you need a slope so rain and snow leave the roof. The 'triangler' roof you see at the end of a house is called a 'Gable roof.' It is triangular mostly because of strength, the triangle is one of the few shapes that can not be distorted with out actually distroying it, the top of a square or rectangle can be pushed over to make a parallelogram. Also strong winds can lift a flat or shed roof, either by just pulling it up, similar to an airplane wing or pushing up from one overhanging edge. The triangle of a ridged roof braces one slope against the other The simplest roof with a slope is a 'shed roof' just a flat roof with one side higher than the other.Flat and shed roofs are easy to build, a shed roof needs a V shaped notch, called a birds mouth, where it rests on the walls, the birds mouths on each end are at the same angles. But flat and sheds have a problem; the 'beams,' or rafters, that go all the way from one side to the other roof have to be very strong, they support not only their own weight but the roof as well, and sometimes the ceiling underneath. They tend to sag in the middle. As the span, distance between the supporting walls, increases the rafters have to be longer, which makes them heavier all by themselves making them sag even more. And they can be pushed to one side. The gable roof is the simplest way that allows me to span a greater distance. They need the birds mouths too, but also the angle at the top where the rafters meet, the ridge, has to be carefully determined, the rafter is slightly longer on the top edge. . Now the weight of the rafter and roof is carried out to the walls, their is still some sag to the rafters but since the whole roof slopes I don't get a water holding dip. Of course the weight tries to spread the walls apart at the top, I can put horizontal braces from the center of each rafter across to the other to fight the sag and the spread. Or I can use the joists that run from the top of the wall over to the other wall and hold the ceiling ( they don't have to be as strong as roof rafters since all they hold is the ceiling) and run angled braces between them and the rafters. That is a truss roof and is very strong, the braces all form triangles. At the end of the house I just extend the wall on up to the bottom of the roof and there is your triangle on top of the wall under the roof. A roof that is triangular and is actually a roof over a wall is called a hip roof, one step more of difficulty.It is similar to a gable roof but the ridge does not run all the way to the end of the house. Usually the ridge ends the same distance from the end as is from the sides of the house.(A hip roof on a square house is a pyramid, a very ugly roof in my opinion.) From the end of the ridge hip rafters run down to each corner of the house, rafters run from the top of the end wall up to the hip rafter. Those rafters have to have a compound angle at the top, not only does the top edge have to be longer but the side towards the ridge has to be longer than the down slope side. A hip roof is stronger than a gable roof, you have triangles bracing triangles, it can withstand higher winds. Speaking of which, sorry to be so long winded, but its raining, HARD, so I can't be out building roofs today. I'm just sitting here watching the rain run off my gable roof and wishing I could be sitting under my shed roofed patio cover, kicking my self for not making more slope on it, cause it leaks in frog drownders like this.

For strength and to get the rain and snow to shed downwards quickly and off the roof. The longer it stays on the surface of the roof, the more risk it could penetrate.

No. They are actually triangular.

There are a few reasons why houses are built with a sloped /pitched roof. Or triangle as you say. Not all buildings and houses are built this way but many houses are built around trees which the slope helps keep debris off of roofs limbs and leafs. also for snow as well as stability. It also helps in high winds allowing the wind to push up and away. The steeper the pitch the faster snow and debris will come off. keeping this added weight off of your roof.