Mathematics

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?

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

2 Answer

  • 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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