Complete the condition statements that must be met in order for three side lengths— a , b , and c —to create a triangle.(1 point)
a __ b+c and a __ b−c
3 answers
a < b+c and a > |b-c|
can you explain how
Sure! In order for three side lengths, a, b, and c, to form a triangle, the sum of the lengths of any two sides must be greater than the length of the third side. This is known as the Triangle Inequality Theorem.
1. The first condition, a < b+c, means that the length of side a is less than the sum of the lengths of sides b and c. This ensures that side a is not too long to connect to sides b and c.
2. The second condition, a > |b-c|, is a bit more complex. The absolute value of the difference between b and c, |b-c|, represents the maximum allowable difference in lengths between sides b and c. The condition a > |b-c| ensures that side a is long enough to connect sides b and c, considering their potential difference in length.
By satisfying both conditions, we ensure that the three side lengths can actually form a closed triangle.
1. The first condition, a < b+c, means that the length of side a is less than the sum of the lengths of sides b and c. This ensures that side a is not too long to connect to sides b and c.
2. The second condition, a > |b-c|, is a bit more complex. The absolute value of the difference between b and c, |b-c|, represents the maximum allowable difference in lengths between sides b and c. The condition a > |b-c| ensures that side a is long enough to connect sides b and c, considering their potential difference in length.
By satisfying both conditions, we ensure that the three side lengths can actually form a closed triangle.