Using the Triangle Inequality Theorem (see picture above), determine the length of the third side of the triangle.
side x equals 1 m
side x equals 2 m
side x equals 13 m
To determine the length of the third side of the triangle, we need to make sure that the sum of the lengths of any two sides of the triangle is greater than the length of the third side.
For the first pair of sides (1m and 2m):
1m + 2m = 3m
Since 3m is greater than 1m, the first pair follows the Triangle Inequality Theorem.
For the second pair of sides (1m and 13m):
1m + 13m = 14m
Since 14m is greater than 2m, the second pair also follows the Triangle Inequality Theorem.
For the final pair of sides (2m and 13m):
2m + 13m = 15m
Since 15m is greater than 1m, the final pair also follows the Triangle Inequality Theorem.
Therefore, the lengths of 1m, 2m, and 13m can form a valid triangle and the length of the third side is 15m.
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According to the Triangle Angle Sum Theorem, the sum of the inside angles of a triangle must be equal to ?
90 degrees
100 degrees
180 degrees
360 degrees
180 degrees
Two angles of a triangle measure 39.5° and 61.7°. Using the Triangle Angle Sum Theorem, which states that the sum of the inside angles of all triangles must equal 180°, find the measure of the third angle.
68.8°
78.8°
88.8°
98.8°
To find the measure of the third angle of the triangle, we first calculate the sum of the given angles:
39.5° + 61.7° = 101.2°
Now, we can find the measure of the third angle by subtracting this sum from 180° (the total sum of the inside angles of a triangle):
180° - 101.2° = 78.8°
Therefore, the measure of the third angle of the triangle is 78.8°.
Use the Triangle Inequality Theorem (see picture above) to solve this problem. Two sides of a triangle measure 11 and 3. Identify the side measure that would NOT create a triangle.
7
9
12
13
To determine which side measure would NOT create a triangle according to the Triangle Inequality Theorem, we can compare the sum of the two sides to the length of the third side.
Given sides of the triangle: 11 and 3
- For the pair of sides (11 and 7):
11 + 7 = 18
Since 18 is greater than 3, this pair satisfies the Triangle Inequality Theorem.
- For the pair of sides (11 and 9):
11 + 9 = 20
Since 20 is greater than 3, this pair also satisfies the Triangle Inequality Theorem.
- For the pair of sides (11 and 12):
11 + 12 = 23
Since 23 is greater than 3, this pair also satisfies the Triangle Inequality Theorem.
- For the pair of sides (11 and 13):
11 + 13 = 24
Since 24 is greater than 3, this pair satisfies the Triangle Inequality Theorem.
Therefore, the side measure that would NOT create a triangle is 7, because it does not satisfy the Triangle Inequality Theorem as a side length of 7 cannot be paired with side lengths of 11 and 3 to form a triangle.