Answer:
Yes, they are similar. The scale factor is 5/3
Step-by-step explanation:
The longest to the shortest side of quadrilateral KLMJ are: JM, ML, KJ, LK
The longest to the shortest side of quadrilateral QPSR are: QP, PS, RQ, SR
If the two quadrilaterals are similar, the following proportion must be satisfied:
JM = k*QP
ML = k*PS
KJ = k*RQ
LK = k*SR
where k is the scale factor. Solving for k and replacing with lengths:
k = 25/15 = 24/14.4 = 20/12 = 15/9 = 5/3
From the figure, we can also see that:
∠M ≅ ∠P
∠L ≅ ∠S
∠R ≅ ∠K
∠Q ≅ ∠J
Therefore, the two quadrilaterals are similar.
