Answer:
AC is greater than BC
Step-by-step explanation:
First, we know that the angle of a straight line is 180°, so angle B as a whole is equal to 180 degrees. Therefore, angle YBC + angle ABC = 180 degrees. As angle YBC is a right angle, signified by the small square on the angle, it is 90 degrees. Therefore,
90 degrees + angle ABC = 180 degrees
subtract 90 degrees from both sides to isolate angle ABC
angle ABC = 90 degrees
Therefore, as angle ABC is equal to 90 degrees, and a right angle is 90 degrees, triangle ABC has a right angle, making it a right triangle.
In a right triangle, using the Pythagorean Theorem, the square of the side opposite the right angle is equal to the sum of the squares of the other side. Since side AC is opposite the right angle, we can say that
AC² = AB² + BC²
As the length of a side has to be greater than 0, we can say that
AC² = AB² + BC²
AB² > 0
AC² > BC²
square root both sides
AC > BC
Therefore, AC is greater than BC
