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
13 answers
a + b > c and a > |b - c|
Use the image to answer the question.
Complete the inequality so that it represents the whole-number values that side a could be to create a triangle.
An illustration of a triangle shows an equation along the base as b equals 6 and the hypotenuse as c equals 7. The third side on the triangle is labeled as a.
(1 point)
_<a<_
Complete the inequality so that it represents the whole-number values that side a could be to create a triangle.
An illustration of a triangle shows an equation along the base as b equals 6 and the hypotenuse as c equals 7. The third side on the triangle is labeled as a.
(1 point)
_<a<_
2 < a < 13
Apply the Triangle Inequality Theorem to determine which three side lengths form a triangle.(1 point)
Responses
20, 10, 30
20, 10, 30
8, 4, 12
8, 4, 12
10, 20, 15
10, 20, 15
8, 8, 20
Responses
20, 10, 30
20, 10, 30
8, 4, 12
8, 4, 12
10, 20, 15
10, 20, 15
8, 8, 20
The three side lengths that form a triangle are:
20, 10, 30 (since 20 + 10 > 30, 20 + 30 > 10, 10 + 30 > 20)
20, 10, 30 (since 20 + 10 > 30, 20 + 30 > 10, 10 + 30 > 20)
Apply the Triangle Inequality Theorem to determine the possible whole number measures of the third side of a triangle if the first two sides measure 6 and 2. List them in ascending order.(2 points)
The measure of the third side could be
,
, or
.
The measure of the third side could be
,
, or
.
The possible whole number measures of the third side of a triangle would be 3, 4, or 5 in ascending order.
In triangle ABD
, AB
is 3 cm
long and BD
is 5 cm
long. According to the Triangle Inequality Theorem, which two lengths are possible lengths of AD
? (1 point)
Responses
7 cm
7 cm
10 cm
10 cm
1 cm
1 cm
2 cm
2 cm
4 cm
, AB
is 3 cm
long and BD
is 5 cm
long. According to the Triangle Inequality Theorem, which two lengths are possible lengths of AD
? (1 point)
Responses
7 cm
7 cm
10 cm
10 cm
1 cm
1 cm
2 cm
2 cm
4 cm
According to the Triangle Inequality Theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Given that AB = 3 cm and BD = 5 cm:
Possible lengths of AD:
1) AD < 3 + 5 -> AD < 8 cm
2) AD > 5 - 3 -> AD > 2 cm
So, the possible lengths of AD are 2 cm and 7 cm.
Given that AB = 3 cm and BD = 5 cm:
Possible lengths of AD:
1) AD < 3 + 5 -> AD < 8 cm
2) AD > 5 - 3 -> AD > 2 cm
So, the possible lengths of AD are 2 cm and 7 cm.
A right triangle has acute angles measuring 2x+6 degrees and 3x−26 degrees. Use the Triangle Angle Sum Theorem to find the measures of the missing angles of the triangle.
The Triangle Angle Sum Theorem states that the sum of the three interior angles of a triangle is always 180 degrees.
In a right triangle, one angle is always 90 degrees. From the problem, we know that the acute angles are 2x+6 degrees and 3x-26 degrees. So, we can set up the equation:
90 degrees + 2x + 6 degrees + 3x - 26 degrees = 180 degrees
Solving for x:
90 + 2x + 6 + 3x - 26 = 180
5x + 70 = 180
5x = 110
x = 22
Now that we have found the value of x, we can substitute it back into the angle expressions to find the measures of the missing angles:
2(22) + 6 = 50 degrees
3(22) - 26 = 46 degrees
Therefore, the measures of the missing angles are 50 degrees and 46 degrees.
In a right triangle, one angle is always 90 degrees. From the problem, we know that the acute angles are 2x+6 degrees and 3x-26 degrees. So, we can set up the equation:
90 degrees + 2x + 6 degrees + 3x - 26 degrees = 180 degrees
Solving for x:
90 + 2x + 6 + 3x - 26 = 180
5x + 70 = 180
5x = 110
x = 22
Now that we have found the value of x, we can substitute it back into the angle expressions to find the measures of the missing angles:
2(22) + 6 = 50 degrees
3(22) - 26 = 46 degrees
Therefore, the measures of the missing angles are 50 degrees and 46 degrees.
.
An illustration shows a triangle with vertices as B C D. Angle C on the top is labeled as a question mark and angle D on the bottom right is labeled as 22 degrees. Vertex B is on the bottom left. The horizontal line D B extends beyond the triangle to the left with an arrow at the end, and a point A is marked on it. The angle of A B C is labeled as 103 degrees.
Use the Triangle Angle Sum Theorem to find the measure of the angle on point C .
An illustration shows a triangle with vertices as B C D. Angle C on the top is labeled as a question mark and angle D on the bottom right is labeled as 22 degrees. Vertex B is on the bottom left. The horizontal line D B extends beyond the triangle to the left with an arrow at the end, and a point A is marked on it. The angle of A B C is labeled as 103 degrees.
Use the Triangle Angle Sum Theorem to find the measure of the angle on point C .
The Triangle Angle Sum Theorem states that the sum of the three interior angles of a triangle is always 180 degrees.
In this case, we know the measure of angle D is 22 degrees and the measure of angle ABC is 103 degrees.
Let's find the measure of angle C:
Angle C = 180 - (Angle B + Angle D)
Angle C = 180 - (103 + 22)
Angle C = 180 - 125
Angle C = 55
Therefore, the measure of angle C is 55 degrees.
In this case, we know the measure of angle D is 22 degrees and the measure of angle ABC is 103 degrees.
Let's find the measure of angle C:
Angle C = 180 - (Angle B + Angle D)
Angle C = 180 - (103 + 22)
Angle C = 180 - 125
Angle C = 55
Therefore, the measure of angle C is 55 degrees.