j = 5 cm , k = 7 cm, and l = 10 cm
In the triangle shown, which shows the correct order of the angle measures from largest to smallest?
Note: Image is not drawn to scale.
Responses
A C, A, BC, A, B
B B, A, CB, A, C
C C, B, AC, B, A
D A, B, C
B, A, C
To determine the correct order of the angle measures from largest to smallest in the triangle, we can use the triangle inequality theorem. According to the 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 j = 5 cm, k = 7 cm, and l = 10 cm, we can analyze the following possibilities:
1. j + k > l
5 cm + 7 cm > 10 cm
This inequality is true, so angle A is the largest angle.
2. k + l > j
7 cm + 10 cm > 5 cm
This inequality is true, so angle C is the second-largest angle.
3. j + l > k
5 cm + 10 cm > 7 cm
This inequality is also true, so angle B is the smallest angle.
From the analysis above, we conclude that the correct order of the angle measures from largest to smallest is:
D) A, B, C