SOLUTION: In an triangle ABC, BC > AB and AC < AB. Which of the statement is always true? (1) angle A > angle B > angle C (2) angle A > angle C > angle B (3) angle B > angle A

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Question 309771: In an triangle ABC, BC > AB and AC < AB. Which of the statement is always true?

(1) angle A > angle B > angle C
(2) angle A > angle C > angle B
(3) angle B > angle A > angle C
(4) angle C > angle B > angle A
(5) angle C > angle A > angle B

Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
BC > AB
AC < AB.

If AC < AB, this means that AB > AC

The two statement can therefore be equivalent to:

BC > AB
AB > AC

These two statements then become equivalent to the following one statement:

BC > AB > AC

In a triangle, if one side is greater than the other side, than the angle opposite the one side is also greater than the angle opposite the other side.

Since:

angle A is opposite BC
angle C is opposite AB
angle B is opposite AC

Then this means that:

angle A > angle C > angle B

That would be selection (2).

SOLUTION: In an triangle ABC, BC > AB and AC < AB. Which of the statement is always true? (1) angle A > angle B > angle C (2) angle A > angle C > angle B (3) angle B > angle A > an