Select the correct answer.

Using triangle ABC, how does extending vertex C further away to the left of vertex B verify the relationship between sides and angles in triangles?

A. by showing that as BC increases, measure of angle A decreases
B. by showing that as BC increases, measure of angle A increases
C. by showing that as BC increases, measure of angle C increases
D. by showing that as BC increases, measure angle A remains the same

1 answer

The correct answer is:

B. by showing that as BC increases, measure of angle A increases

Explanation:
When you extend vertex C further away to the left of vertex B, you are increasing the length of side BC. According to the properties of triangles, specifically the Law of Sines and the Law of Cosines, as one side of a triangle increases, the angle opposite that side will also increase. Therefore, as side BC increases in length, the measure of angle A (which is opposite side BC) will also increase.
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