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

Answer 1

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 2

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

Explanation:

Given: Δ MNO ≅ Δ RST

∠R = 90°

Slope of RS =
`(-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=(-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* m_2=-1`

`(-1)/(5)* m_2=-1`

`m_2=-1*-5`

`m_2=5`

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