Here is a list of triples, three numbers in a set. Determine if the three numbers could be the lengths of triangle sides, and if so, classify the triangle by both classification types,
Classification by biggest angle: Obtuse, Right, Acute
Classification by side length relations: Isosceles, Equilateral, Scalene
a) 6, 3, 3
b) 7, 4, 1
c) 5, 5, 2
d) 5, 4, 3
e) 4, 4, 4
Answers in the comments.
a) 6, 3, 3
ReplyDeleteTechnically, this would make a line segment, but by the rules set by the Triangle Inequality, we will call this a triangle.
Isosceles because two sides of length 3
Obtuse because 6² > 3² + 3²
b) 7, 4, 1
4 + 1 < 7, so not a triangle
c) 5, 5, 2
Isosceles because two sides of length 5
Acute because 5² < 5² + 2²
d) 5, 4, 3
Scalene because all sides different
Right because 5² = 4² + 3²
e) 4, 4, 4
Equilateral because all sides equal
Acute because 4² > 4² + 4²
To figure out the triangle inequality which is : a + b greater or equal c greater or equal to | a - b |
ReplyDeleteAccording to your examples, it does not matter the sequence of the numbers?
Should we multiply the numbers first in order to see if it even a triangle and then figure out whether it's equilateral acute?
Do we always put the larger number to the on the other side of the greater then or less?
First see if it's a triangle. In the Triangle Inequality, any order will work. No multiplication in this formula.
ReplyDeleteWhen checking the sums of squares, now we need c to be the largest of the lengths.
Made a mistake in answer e). The sign should be the less than sign, not the greater than sign. All the rest of it is correct.
ReplyDeletee) 4, 4, 4
Equilateral because all sides equal
Acute because 4² < 4² + 4²
thanks
ReplyDelete