As per the Triangle Inequality Theorem, since GJ < GH < HJ, the corresponding angles follow ∠G < ∠H < ∠J. Here option C is correct.
To determine the relationship between the angles in triangle GHJ, we can use the Triangle Inequality Theorem and consider the side lengths GH, HJ, and GJ.
The Triangle Inequality Theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
In this case:
GH + GJ > HJ (21 + 9 > 24) is true.
GH + HJ > GJ (21 + 24 > 9) is true.
HJ + GJ > GH (24 + 9 > 21) is true.
Since all three inequalities hold, triangle GHJ is valid.
Now, let's analyze the angles:
∠G is opposite side HJ.
∠H is opposite side GJ.
∠J is opposite side GH.
Considering the given side lengths:
GJ < GH < HJ.
This implies that ∠G < ∠H < ∠J. Therefore, the correct statement is ∠ H is the largest. Here option C is correct.
Complete question:
in △ GHJ, GH=21 inches, HJ=24 inches, and GJ=9 inches. Which statement is true?
A. ∠ G is the smallest
B. ∠ J is the smallest
C. ∠ H is the largest
D. ∠ G is the largest.