Question

Which additional fact proves that ΔRST and ΔWXY are congruent if ∠T ≅ ∠Y and RT ≅ WY?

Answer 1

Answer:

Hence, option A is correct.

Step-by-step explanation:

We are asked to find the fact such that ΔRST and ΔWXY are congruent.

Since, we are given: ∠T ≅ ∠Y  and  RT ≅ WY.

we are given the following assumptions:

∠W = x + 5  

∠X = 3x - 9

∠Y = 2x + 4

as we are given one angle congruent and one side congruent so in order to prove two triangles are congruent we just need to show that one more pair of angles are congruent.

so from the two triangle we could have that ∠W≅∠R

and ∠X≅∠S

Now we will go by options:

A)

if ∠S=2x+20 then as ∠X≅∠S.

3x-9=2x+20

x=29

∠S=∠W=78°.

B)

if ∠R = 2x + 20 then as  ∠W≅∠R

⇒  x+5=2x+20

⇒ x= -15 which is not possible as it will make measure of angle W negative (x+5= -15+5= -10)

C)

if ∠S=2x^2+5 then as  ∠X≅∠S.

⇒ 3x-9=2x^2+5

⇒ 2x^2-3x+14=0

on solving this quadratic equation we will get complex zeros.

Hence, option (C) is not correct.

D)

if ∠R =  2x

^2

+ 5 then as ∠W≅∠R.

⇒ x+5=

2x

^2

+ 5

⇒ 2x^2-x=0

⇒ x(2x-1)=0

either x=0 or x=1/2 which is not  possible.

because by putting this x value in all the angles we see that sum of all the angles of a triangle is not equal  to 180°

Hence, option D is not possible.

Hence, option A is correct.