Complete the condition statements that must be met in order for three sides length—a,b and c— to create a triangle.
a ( ) b+c and a ( ) b-c
a > |b-c| and a < b+c
Complete the inequality so that it represents the whole-number values that side a could be to create a triangle
C= 7
B= 6
() < a < ()
In order for side a to form a triangle with sides b=6 and c=7, the inequality is:
2 < a < 13
Apply the triangle inequality theorem to determine which the side lengths form a triangle
10,20,15
20,10,30
8,4, 12
8,8,20
According to the triangle inequality theorem, in a triangle, the sum of the lengths of any two sides must be greater than the length of the third side.
1. For the side lengths 10, 20, and 15:
- 10 + 15 = 25 > 20 (True)
- 10 + 20 = 30 > 15 (True)
- 20 + 15 = 35 > 10 (True)
--> These side lengths form a triangle.
2. For the side lengths 20, 10, and 30:
- 20 + 10 = 30 > 30 (False)
--> These side lengths do not form a triangle.
3. For the side lengths 8, 4, and 12:
- 8 + 4 = 12 > 12 (False)
--> These side lengths do not form a triangle.
4. For the side lengths 8, 8, and 20:
- 8 + 8 = 16 > 20 (False)
--> These side lengths do not form a triangle.
Apply the triangle inequality theorem to determine the possible whole number measures of the third side of a triangle of the first two sides measure 6 and 2. List them in ascending order
To determine the possible whole number measures of the third side of a triangle where the first two sides are 6 and 2, we can apply the triangle inequality theorem:
Let the first two sides be a=6 and b=2.
According to the triangle inequality theorem, for a triangle to exist:
- The sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Now, we can set up the inequality based on the given sides:
2 < a+b < 6+2
2 < a+b < 8
2 < 6+2 < 8
2 < 8 < 8
Therefore, the possible whole number measures of the third side are: 3, 4, 5, 6 and 7, listed in ascending order.
There is a number line A is on -4, B is on -1, C is on 3 and D is on 4
A triangle has no congruent sides. The length of two sides of the triangle are AB and BD. Use the number line above to determine the length of AB and BD. Then, use the triangle inequality theorem to determine which two segments have lengths that could be used as the third side of the triangle. Select a response containing 2 possible answers
BC and CD
CD and AC
BC and AD
AC and BC
To determine the lengths of AB and BD, we calculate the distances between the points on the number line.
AB would be the distance between A and B:
AB = distance from -4 to -1 = |-4 - (-1)| = 3 units
BD would be the distance between B and D:
BD = distance from -1 to 4 = |(-1) - 4| = 5 units
Now, let's consider the lengths that could be used as the third side of the triangle based on the Triangle Inequality Theorem:
For a triangle to be formed:
- The sum of the lengths of any two sides must be greater than the length of the third side.
Potential side lengths that make a triangle (based on the triangle inequality theorem) are:
- BD and CD: 5 + 1 > 3 (True)
- CD and AC: 1 + 7 > 5 (True)
Thus, the two possible side lengths that could form the third side of the triangle are BC and CD.
A right triangle has a score measuring 2x + 6 degrees and 3x - 26 degrees. Use the triangle angle sum theorem to find the measure of the missing angle of the triangle
In a triangle, the sum of the three interior angles is always 180 degrees.
Given that the two angles in the right triangle are 2x + 6 and 3x - 26 degrees, and one angle is a right angle (90 degrees), we can use the Triangle Angle Sum Theorem to find the measure of the missing angle.
The sum of the three angles in the triangle is:
(2x + 6) + (3x - 26) + 90 = 180
Combine like terms:
5x - 20 + 90 = 180
5x + 70 = 180
5x = 110
x = 22
Now, substitute x back into the expressions for the given angles to find their measures:
2(22) + 6 = 50 degrees
3(22) - 26 = 40 degrees
Now, find the measure of the missing angle:
Missing angle = 180 - (50 + 90 + 40) = 180 - 180 = 0 degrees
Therefore, the measure of the missing angle in the right triangle is 0 degrees.