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_b+c and a_b−c

Answer 1

[AI-generated answer — Bot GPT 3.5]

a + b > c and a > |b - c|

Answer 2

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<_

Answer 3

[AI-generated answer — Bot GPT 3.5]

2 < a < 13

Answer 4

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

Answer 5

[AI-generated answer — Bot GPT 3.5]

The three side lengths that form a triangle are:

20, 10, 30 (since 20 + 10 > 30, 20 + 30 > 10, 10 + 30 > 20)

Answer 6

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
.

Answer 7

[AI-generated answer — Bot GPT 3.5]

The possible whole number measures of the third side of a triangle would be 3, 4, or 5 in ascending order.

Answer 8

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

Answer 9

[AI-generated answer — Bot GPT 3.5]

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.

Answer 10

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.

Answer 11

[AI-generated answer — Bot GPT 3.5]

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.

Answer 12

.

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 .

Answer 13

[AI-generated answer — Bot GPT 3.5]

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.