Question

in triangle ABC, measurement of Angle C=90 and line AC is congruent to line BC. If AB=12, find AC

Answer 1

Congruent means the "same" So if you have an angle of 90 you know you have a right triangle....but since we also know that 2 lines are the same...we know it is a 45 45 90 triangle



In a 45 45 90 triangle..the hypotenuse (the longest side so AB for you) would be the result of one of the smaller legs times √2



So we need to find out...WHAT times the √2 = 12

\[\large x \times √2 = 12\]
\[\large x = \frac{12}{√2}\]
\[\large x = \frac{12√2}{√2√2}\]
\[\large x = \frac{12√2}{2}\]
\[\large x = 6√2\]

That is what you AC equals

Answer 2

oh I was not sure if I was going down the right path thank you

Answer 3

No problem!