Question

state if the polygons are similar. yes = similar, no = not similar.
1)
two parallelograms: first with sides 12, 8, 12, 8 and a 65° angle; second with sides 18, 12, 18, 12 and a 65° angle.
2)
two parallelograms: first with sides 20, 20, 20, 20 and a 110° angle; second with sides 15, 15, 15, 15 and a 70° angle.
3)
two parallelograms: first with sides 12, 12, 12, 12 and a 40° angle; second with sides 18, 18, 18, 18 and a 130° angle.
4)
two parallelograms: first with sides 16, 28, 16, 28 and a 60° angle; second with sides 4, 4, 4, 4 and a 120° angle.
5)
two parallelograms: first with sides 12, 8, 12, 8 and a 75° angle; second with sides 18, 12, 18, 12 and a 70° angle.
6)
two parallelograms: first with sides 9, 18, 9, 18 and a 55° angle; second with sides 4, 6, 4, 6 and a 55° angle.
7)
two parallelograms: first with sides 12, 18, 12, 18 and a 50° angle; second with sides 16, 24, 16, 24 and a 45° angle.

Explanation:

Step1: Check similarity for 1)

First, verify side ratios: $\frac{8}{12}=\frac{2}{3}$, $\frac{12}{18}=\frac{2}{3}$. Corresponding angles are equal ($65^\circ$).

Step2: Check similarity for 2)

Side ratios: $\frac{20}{15}=\frac{4}{3}$, but angles: $110^\circ
eq 70^\circ$.

Step3: Check similarity for 3)

Side ratios: $\frac{12}{18}=\frac{2}{3}$, but angles: $40^\circ
eq 130^\circ$.

Step4: Check similarity for 4)

Side ratios: $\frac{16}{4}=4$, $\frac{28}{4}=7$. Ratios are not equal.

Step5: Check similarity for 5)

Side ratios: $\frac{8}{12}=\frac{2}{3}$, $\frac{12}{18}=\frac{2}{3}$. Angles: $75^\circ
eq 70^\circ$.

Step6: Check similarity for 6)

Side ratios: $\frac{9}{4}
eq\frac{18}{6}=3$. Ratios are not equal.

Step7: Check similarity for 7)

Side ratios: $\frac{12}{16}=\frac{3}{4}$, $\frac{18}{24}=\frac{3}{4}$. Corresponding angles are equal ($50^\circ$).

Answer:

1. Yes = Similar
2. No = Not Similar
3. No = Not Similar
4. No = Not Similar
5. No = Not Similar
6. No = Not Similar
7. Yes = Similar