Questions: Given parallelogram UVWX below. If UY=19, find YW.

Transcript text: Given parallelogram $U V W X$ below. If $U Y=19$, find $Y W$.

Solution

Solution Steps

Step 1: Identify the properties of the parallelogram

In a parallelogram, the diagonals bisect each other. This means that each diagonal is divided into two equal parts at the point where they intersect.

Step 2: Apply the property to the given problem

Given that $ UY = 19 $, and knowing that $ UY $ is half of the diagonal $ UX $ because the diagonals bisect each other, we can determine the length of $ UX $.

Step 3: Calculate the length of $ UX $

Since $ UY $ is half of $ UX $: \[ UX = 2 \times UY \] \[ UX = 2 \times 19 \] \[ UX = 38 \]

Step 4: Determine the length of $ YW $

Similarly, $ YW $ is half of the diagonal $ WX $. Since $ UX $ and $ WX $ are equal in length (as diagonals of a parallelogram bisect each other and are equal in length): \[ YW = \frac{UX}{2} \] \[ YW = \frac{38}{2} \] \[ YW = 19 \]

Final Answer

\[ YW = 19 \]

Was this solution helpful?

Unhelpful

Helpful

Questions asked by other users

< Previous Next >