Question
If AB < AC < CB in ΔABC, then which of the following is true?
(1 point)
Responses
m∠A < m∠B < m∠C
m ∠ A < m ∠ B < m ∠ C
m∠C < m∠A < m∠B
m ∠ C < m ∠ A < m ∠ B
m∠C < m∠B < m∠A
m ∠ C < m ∠ B < m ∠ A
m∠A < m∠C < m∠B
m∠A < m∠C < m∠B
In ΔABC, if AB < AC < CB, then the correct statement is:
m∠C < m∠A < m∠B
To determine which of the given statements is true, we need to consider the relationship between the angles in the triangle.
In triangle ABC, we are given that AB < AC < CB. This implies that side AB is the smallest side, while side CB is the largest side.
When comparing angles, we know that the angle opposite the largest side is the largest angle. Therefore, angle ∠C is the largest angle since it is opposite the largest side CB.
Similarly, the angle opposite the smallest side is the smallest angle. Therefore, angle ∠A is the smallest angle since it is opposite the smallest side AB.
So, we can conclude that m∠A < m∠C < m∠B is the correct statement.