Question

DUE SOON PLEASE HELP

Are any of the Triangles shown below mathematically similar?
Please demonstrate your knowledge of similar triangles by a written
explanation of your answer using mathematical reasoning. The relationship
between each of the three triangles is worth 5 points each.

(I know that Triangle PRQ is 180-80-20= 80 degrees for angle P. I’m stuck on the other two triangles)

Answer 1

Explanation:

ΔVWX is an isosceles triangle.

∠V ≅∠W = 20

20 + 20 + ∠X = 180

∠X = 180 - 40

∠x = 140

In ΔPQR

∠P + 20 + 80 = 180 {Angle sum property of triangle}

∠P + 100 = 180

∠P = 180 - 100

∠P = 80

In ΔSTV is an isosceles triangle.

∠S ≅ ∠T = 80°

∠V + 80 + 80 = 180

∠V + 160 = 180

∠V = 180 - 160

∠V = 20°

In ΔPRQ & ΔSTV

∠P ≅ ∠S = 80°

∠R ≅ ∠T = 80°

∠Q ≅ ∠v = 20°

ΔPRQ ` ΔSTV are similar by AAA congruent