Since all angles of a rectangle are right angles and all right angles are congruent, we know that the corresponding angles must be congruent. Remember that shorter sides correspond with the shorter sides, and the longer ones with the longer ones.
∠ F ≅ ∠ Q
∠ G ≅ ∠ R
∠ H ≅ ∠ S
∠ J ≅ ∠ T
Comparing the Ratios
Now, let's compare the ratios of the corresponding sides. Recall that the included side between a pair of angles of one polygon corresponds to the included side between the corresponding pair of congruent angles of another polygon.
Corresponding Sides
Ratio
Substitute Lengths
Simplify
F G, Q R
FG/QR
9/21
3/7
G H, R S
GH/RS
4/10
2/5
H J, S T
HJ/ST
9/21
3/7
J F, T Q
JF/TQ
4/10
2/5
As we can see, the ratios are not equal. Therefore, the given rectangles are not similar.
