Consider the two triangles. how can the triangles be proven similar by the sas similarity theorem? show that the ratios are equivalent, and ∠u ≅ ∠x. show that the ratios are equivalent, and ∠v ≅ ∠y. show that the ratios are equivalent, and ∠w ≅ ∠x. show that the ratios are equivalent, and ∠u ≅ ∠z.

In SAS similarity theorem if two sides of one triangle are proportional to two sides of another triangle and angle between them are congruent then the triangle are similar.

Step-by-step explanation:

From SAS similarity theorem-two triangles are similar if all their corresponding angles are congruent and their corresponding sides are proportional.

Now, we check the similarity from SAS , if two sides of first triangle are proportional to two sides of another triangle and angle between them are congruent.

From triangle   UVW and triangle XYZ

Use sides UV and UW in Δ UVW  and XY and XZ in ΔXYZ  .

and angle between them  .

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240