Question

How can the triangles be proven similar by the SSS similarity theorem? Show that the ratios StartFraction U V Over X Y EndFraction , StartFraction W U Over Z X EndFraction , and StartFraction W V Over Z Y EndFraction are equivalent. Show that the ratios StartFraction U V Over Z Y EndFraction , StartFraction W U Over Z X EndFraction , and StartFraction W V Over X Y EndFraction are equivalent. Show that the ratios StartFraction U V Over X Y EndFraction and StartFraction W V Over Z Y EndFraction are equivalent, and ∠V ≅ ∠Y. Show that the ratios StartFraction U V Over Z Y EndFraction and StartFraction W U Over Z X EndFraction are equivalent, and ∠U ≅ ∠Z. Consider the two triangles

Answer 1

Answer:

option 1

Step-by-step explanation:

The question is as shown in the attached figure.

From the figure, we can deduce that:

∠U ≅ ∠X and ∠W ≅ ∠Z  and ∠V ≅ ∠Y

So, ΔUWV similar to ΔXZY

But it is required to know " How can the triangles be proven similar by the SSS similarity theorem? "

So, we need to prove the corresponding angles are proportion

With the help of the previous corresponding angles.

So, we need to show that the ratios $\frac{UV}{XY} \ , \ \frac{WU}{ZX} \ and \ \frac{WV}{ZY}$ are equivalent.

So, the answer is option 1

Answer 2

To prove that ΔUVW and ΔXYZ are similar by the SSS Similarity Theorem: a. show that the ratios UV/XY, WU/ZX, and WV/ZY are equivalent.

What is the SSS Similarity Theorem?

The SSS Similarity Theorem states that two triangles are similar if the ratio of all three pairs of corresponding sides of two triangles are equivalent.

Given ΔUVW and ΔXYZ, where:

• UV corresponds with XY, thus UV/XY = 50/40 = 1.25
• WU corresponds with ZX, thus WU/ZX = 40/32 = 1.25
• WV corresponds with ZY, thus WV/ZY = 60/48 = 1.25

Since all the ratio of all three corresponding sides of both triangles are equivalent, therefore both triangles can be proven to be similar by the SSS Similarity Theorem.

Therefore, to prove that ΔUVW and ΔXYZ are similar by the SSS Similarity Theorem: a. show that the ratios UV/XY, WU/ZX, and WV/ZY are equivalent.

Learn more about the SSS Similarity Theorem on:

https://brainly.com/question/4163594