Question

Triangle MNO is congruent to right triangle RST with a right angle at vertex R. If the slope of RS is -1/5, what must be true?

Answer 1

Answer:

Option 1 must be true .i.e., Slope of TR is 5

Step-by-step explanation:

Given: Δ MNO ≅ Δ RST

          ∠R = 90°

          Slope of RS =  $\frac{-1}{5}$

We are given ΔMNO is congruent to ΔRST but we are not told which side is equal to which side.

Means in ΔRST we know ∠R is right angle but in ΔMNO we dont know which angle is right angle.

⇒ We can't say anything about slopes of sides of ΔMNO.

Therefore, Option 2 , 3 , 4 can be true but not sure.

But, in ΔRST

∠R is right angle means RS ⊥ RT

Slope of RS, $m_1=\frac{-1}{5}$

Let Slope of RT be $m_2$

We know that product of slopes of perpendicular lines are equal to -1.

$\implies m_1\times m_2=-1$

$\frac{-1}{5}\times m_2=-1$

$m_2=-1\times-5$

$m_2=5$

Therefore, Option 1 must be true .i.e., Slope of TR is 5

Answer 2

The best and the most correct answer among the choices provided by the question is the first choice. The statement that is true is "The slope of TR is 5". I hope my answer has come to your help. God bless and have a nice day ahead!