Question

Which additional fact proves that ΔRST and ΔWXY are congruent if ∠R ≅ ∠W and RS ≅ WX. ∠R = 2x + 5 ∠S = 4x + 10 ∠T = 2x - 11

Answer 1

Additional fact proves that ΔRST and ΔWXY are congruent :  D) ∠Y = x / 2 + 22

Further explanation

Triangles are said to be congruent if :

• 1. all three sides equal (SSS ---> side, side, side)

• 2. two sides and the included angle of 2 triangles, are equal (SAS -> Side, Angle, Side)

• 3. If the two angles and the included sides of the 2 triangles are equal (ASA -> Angle, Side, Angle)

• 4. If the two angles and the non-included sides of 2 triangles are equal (AAS -> Angle, Angle, Side)

We complete the available answer choices

 A) ∠X = 9x / 2

  B) ∠Y = 9x / 2

  C) ∠X = x / 2 + 22

  D) ∠Y = x / 2 + 22

 

Total of angles in triangle = 180°

∠R + ∠S + ∠T = 180 °

(2x + 5) + (4x + 10) + (2x-11) = 180°

8x + 4 = 180 °

8x = 176 °

x = 22 °

So,

∠R = 2x + 5 = 2.22+ 5 = 49 °

∠S = 4x + 10= 4.22 + 10 = 98 °

∠T = 2x - 11 = 2.22 - 11 =33 °

If both triangles are congruent then  :

∠R≅∠W, or ∠S≅∠X, or ∠T≅∠Y

Let check the equation from answer option :

A) ∠X = 9x / 2  = 9.22 : 2 = 99°, not true

  B) ∠Y = 9x / 2  = 9.22 : 2 = 99°, not true

  C) ∠X = x / 2 + 22  = 22:2 + 22 = 33°

  D) ∠Y = x / 2 + 22  = 22:2 + 22 = 33°

Both triangles congruent with AAS theorem,

∠R≅∠W, ∠T≅∠Y and RS ≅ WX

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Keywords :Keywords : triangle, the AAS Similarity , side, similar,angles,SAS,ASA,AAS,SSS

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Answer 2

Answer:

The answer is option D. x/2+22