If AB < AC < CB in ABC, then which of the following is true? Hint: draw a picture to help you! (1 point)
O mzA < m<B < mcC
• mzA < m<C < m<B
O mcC < mzB < mZA
• mcC < mzA < m<B
Based on the given information, we can draw a triangle ABC where AB is shorter than AC and AC is shorter than CB:
A
/\
/ \
/ \
/ \
/ \
/__________\
B C
Now, we need to determine which of the given statements is true. Let's go through each option:
1) mzA < m<B < mcC
Looking at the triangle, we notice that angle A is opposite side BC, angle B is opposite side AC, and angle C is opposite side AB. Since AB < AC < CB, it means that angle B is the smallest angle in the triangle. Therefore, option 1 is not true.
2) mzA < m<C < m<B
Since option 1 is not true, option 2 is automatically the correct answer.
3) mcC < mzB < mZA
This option does not match the given inequality AB < AC < CB, so it is not true.
4) mcC < mzA < m<B
Looking at the triangle, we can see that angle A is opposite side BC. Since AB < AC < CB, it means that angle A is the largest angle in the triangle. Therefore, option 4 is not true.
Thus, the correct answer is:
• mzA < m<C < m<B