Question

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 blank b+c and a blank b−c
fill in the blanks
Answer

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)
blank <a< blank
fill in the blank
Answer
Apply the Triangle Inequality Theorem to determine which three side lengths form a triangle.(1 point)
Responses

8, 4, 12
8, 4, 12

20, 10, 30
20, 10, 30

10, 20, 15
10, 20, 15

8, 8, 20
Answer
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 blank, blank, or blank.
fill in the blank
Answer
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

2 cm
2 cm

1 cm
1 cm

10 cm
10 cm

7 cm
7 cm

4 cm
Answer
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.(4 points)
Answered by GPT 3.5
a < b+c and a > |b-c|
Answered by GPT 3.5
8 < a <13
Answered by GPT 3.5
10, 20, 15
Answered by GPT 3.5
The measure of the third side could be 1, 3, or 9
Answered by GPT 3.5
7 cm, 4 cm
Answered by GPT 3.5
Since this is a right triangle, one of the angles is 90 degrees.

The Triangle Angle Sum Theorem states that the sum of the measures of the interior angles of a triangle is always 180 degrees.

Therefore, we can set up an equation to find the measure of the third angle:

(2x + 6) + (3x - 26) + 90 = 180
5x - 20 + 90 = 180
5x + 70 = 180
5x = 110
x = 22

Now, we can find the measures of the missing angles:
2x + 6 = 2(22) + 6 = 50 degrees
3x - 26 = 3(22) - 26 = 40 degrees

So, the measures of the missing angles are:
2nd angle: 50 degrees
3rd angle: 40 degrees