Bunuel wrote:

Consider the accompanying diagram. Which of the following statements is true?

(A) KM < KL

(B) KM < LM

(C) KL + LM < KM

(D) KL < LM

(E) LM < KL

Attachment:

2017-10-29_1207.png

Triangle property: side lengths correspond with opposite angle measures. The longest side is opposite from the greatest angle. The shortest side is opposite from the smallest angle.

∠ L = 90

∠ M = 55

∠ K = 35

(90+55) = 145; (180-145) = ∠ K

Side opposite ∠ L, 90, is KM

Side opposite ∠ M, 55, is KL

Side opposite ∠ K, 35, is LM

Construct a compound inequality where sides opposite angles are listed from smallest to greatest

35 < 55 < 90, so

LM < KL < KM

Fastest way: look for shortest side, LM, on LHS (all signs are <).

That is Answer E, LM < KL

But (C) must be checked. Different format.

(C) KL + LM < KM

NO. Violates the triangle inequality rule: the sum of any two sides must be greater than the third side.

Answer E

To check others:

(A) KM < KL

NO. Inequality says opposite. And 90 (angle opposite side KM) is not less than 55 (opposite KL)

(B) KM < LM

NO. Inequality says opposite. And 90 is not less than 35

(D) KL < LM

NO. Inequality says opposite. And 55 is not less than 35

Answer E

_________________

In the depths of winter, I finally learned

that within me there lay an invincible summer.

-- Albert Camus, "Return to Tipasa"