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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?

The slope of TR is 5
The slope of OM is 5
The slope of MN is -1/5
The slope of NO is 1/5

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MissPhiladelphia
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!

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 =  [tex]\frac{-1}{5}[/tex]

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, [tex]m_1=\frac{-1}{5}[/tex]

Let Slope of RT be [tex]m_2[/tex]

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

[tex]\implies m_1\times m_2=-1[/tex]

[tex]\frac{-1}{5}\times m_2=-1[/tex]

[tex]m_2=-1\times-5[/tex]

[tex]m_2=5[/tex]

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

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