Question

triangle lkj is similar to triangle tsr. which of the statements is true?
a. the slope of \\(\overline{jl}\\) is equal to the slope of \\(\overline{sr}\\).

b. the slope of \\(\overline{kj}\\) is equal to the slope of \\(\overline{rt}\\).

c. the slope of \\(\overline{jl}\\) is equal to the slope of \\(\overline{rt}\\).

d. the slope of \\(\overline{kj}\\) is equal to the slope of \\(\overline{ts}\\).

Explanation:

Step1: Analyze the triangles' sides

Since \(\triangle LKJ \sim \triangle TSR\), corresponding sides are parallel or have the same slope (as they lie on the same line or parallel lines). \(\overline{JL}\) and \(\overline{RT}\) are both along the same line (the blue line), so their slopes should be equal. Let's check each option:

• Option A: \(\overline{JL}\) is on the blue line, \(\overline{SR}\) is horizontal (slope 0), not equal.
• Option B: \(\overline{KJ}\) is horizontal (slope 0), \(\overline{RT}\) is on the blue line (non - zero slope), not equal.
• Option C: \(\overline{JL}\) and \(\overline{RT}\) are on the same line, so their slopes are equal.
• Option D: \(\overline{KJ}\) is horizontal (slope 0), \(\overline{TS}\) is vertical (undefined slope), not equal.

Answer:

C. The slope of \(\overline{JL}\) is equal to the slope of \(\overline{RT}\)