Conditions for a Unique Triangle
Basics on the topic Conditions for a Unique Triangle
Learn about the different conditions for a unique triangle.
Transcript Conditions for a Unique Triangle
Penny wants to build a new garden bed in the shape of a triangle but needs to figure out what size to make it. If this is going to be a special one-of-a-kind garden bed, we must learn the conditions for a unique triangle. Let's first review what we already know about constructing triangles. The angles in the triangle must add to one hundred eighty degrees. The sum of the two shortest side lengths must be greater than the length of the longest side. If any of these conditions are not met, our triangle would be considered impossible. Penny knows the angle measurements of her triangular area, but not the side lengths. A non-unique triangle occurs when only the angle measurements are given. Non-unique triangles have infinite triangular possibilities. A triangle is unique when only the side lengths are known, and the angles still must add to one hundred eighty. Unique triangles are one of a kind, and only one triangle will exist under these conditions. Let's see if we can classify some triangles using the labels 'non-unique', 'unique', or 'impossible'. For the first triangle, what would we classify this triangle as? The sum of the angles is equal to one hundred eighty degrees, making this triangle possible. Because we do not know the side lengths, this is a 'non-unique triangle' because there are endless options for size. In the next triangle, we are given the side lengths of five feet, seven feet, and nine feet how would we classify this triangle? The rule is that the two shorter sides must add to more than the longest side. The sum of five and seven is twelve, which is greater than nine. This triangle is possible and also unique because when we know the lengths of the sides, only one triangle can be constructed. In the third triangle, the angle measurements of ninety degrees, ten degrees, and seventy degrees are given. How would we use these measurements to determine the triangle classification? The sum of these angles is one hundred seventy degrees so this triangle is impossible. Back to Penny and her triangular-shaped garden bed, where she only knows the angle measurements of thirty-seven degrees, fifty-three degrees, and ninety degrees. We know the triangle is possible since the sum of the angles is one hundred eighty. Is the triangle unique, or non-unique? This triangular area is non-unique and she has unlimited options for how big the triangle can be with the given angle measurements. Penny finds some wood planks for the sides with lengths of three feet, four feet, and five feet. This triangle is possible, the sum of three and four is greater than five. Is this triangle unique or non-unique? It is unique because only one triangle can be formed with these side lengths. Penny has found the measurements for her unique triangular-shaped garden that is one-of-a-kind. Let's summarize! Unique triangles are formed when we know the side lengths, and the angles add up to one hundred eighty. Non-unique triangles are formed when we only know the angle measurements, and they add up to one hundred eighty. Remember, if either of the conditions is false, then the triangle is impossible! "Wow Luis, I guess you were prepared for a non-unique triangular garden bed!"