Guided Practice #2
Your Turn #3
Polygons PQRS and WXYZ are similar. Find the scale factor of polygon PQRS to polygon WXYZ. Then find the values of x and y.
Solution: Let's start by finding the scale factor. To find the scale factor, we need two sides for which we have values. We have values for QR and XY.
Ok, now let's set up the ratio. Remember, the polygon listed first in the problem should be listed on top in the ratio.
Answer: 3/2.4
Put the ratio in decimal form.
Answer: 1.25
Scale Factor: 1.25
Solution: Ok, now that we have the scale factor, we can set up the ratio to solve for x. Which segment has a length of x? ___
Answer: WX
Which side on PQRS is the corresponding side? ___
Answer: PQ
Ok, now we can solve the proportion.
Start by setting the proportion to the side equal to the scale factor we found.
Answer: PQ/WX
Substitute in the values of the sides for PQ and WX.
Answer: 5/x
Eliminate the denominator on the left.
Answer: x, x
Simplify and divide each side to isolate x.
What is your answer?
Answer: 4 = x
Scale factor: 1.25, x = 4
Solution: Now let's solve for y. y represents an angle measurement. How are the angles of similar polygons related?
- They are congruent
- They are proportional
Answer: They are congruent
Correct! They are congruent. Now, which angle on WXYZ corresponds to ∠R? ∠___
Answer: ∠Y
Great! What is the measure of ∠Y?
So, y = ___°
Answer: 125°
