Question

riddle time
determine whether each set of triangles is similar and why.
#1
j. yes, sss
k. not similar
l. yes, sas
m. yes, aa
#2
p. yes, sss
q. yes, aa
r. yes, sas
s. not similar
#3
w. not similar
x. yes, sas
y. yes, sss
z. yes, aa
#4
n. not similar
o. yes, sss
p. yes, sas
q. yes, aa
#5
p. not similar
q. yes, sss
r. yes, sas
s. yes, aa
#6
o. yes, sss
p. yes, asa
q. not similar
r. yes, aa
#7
k. yes, sas
l. yes, sss
m. yes, aa
n. not similar
#8
d. yes, aa
e. not similar
f. yes, sas
g. yes, sss
#9
l. not similar
m. yes, sss
n. yes, aa
o. yes, sas
#10
l. yes, sas
m. yes, sss
n. not similar
o. yes, aa
#11
b. not similar
c. yes, sss
d. yes, aa
e. yes, sas
#12
e. yes, aa
f. yes, sas
g. not similar
h. yes, sss
what was the blackbird doing in the school library?
____ __ ____!
7 6 10 1 4 12 8 10 2 11 10 6 1 3 10 2 9 5

Explanation:

Step1: Analyze #1 (SSS similarity)

Check side ratios:
$\frac{8}{24}=\frac{1}{3}$, $\frac{7}{21}=\frac{1}{3}$, $\frac{14}{39}=\frac{14}{39}$
Since $\frac{1}{3}
eq \frac{14}{39}$, triangles are not similar. Match: K. Not Similar

Step2: Analyze #2 (SAS similarity)

Check included angle + sides:
$\angle Q = \angle U = 48^\circ$, $\frac{88}{48}=\frac{11}{6}$, $\frac{88}{48}=\frac{11}{6}$
Ratios are equal, included angles match. Match: R. Yes, SAS

Step3: Analyze #3 (AA similarity)

Calculate missing angles:
$\triangle NMF$: $180-68-44=68^\circ$; $\triangle GFB$: $180-65-47=68^\circ$
Two pairs of equal angles. Match: Z. Yes, AA

Step4: Analyze #4 (AA similarity)

Right angles + shared angle:
$\angle B = \angle C = 90^\circ$, $\angle R$ is shared. Two equal angle pairs. Match: Q. Yes, AA

Step5: Analyze #5 (AA similarity)

Two pairs of equal angles:
$\angle M = \angle D$, $\angle C = \angle E$. Two equal angle pairs. Match: S. Yes, AA

Step6: Analyze #6 (SSS similarity)

Check side ratios:
$\frac{110}{121}=\frac{10}{11}$, $\frac{18}{20}=\frac{9}{10}$, $\frac{20}{22}=\frac{10}{11}$
Ratios are not all equal. Match: Q. Not Similar

Step7: Analyze #7 (SSS similarity)

Check side ratios:
$\frac{20}{56}=\frac{5}{14}$, $\frac{21}{28}=\frac{3}{4}$, $\frac{42}{44}=\frac{21}{22}$
Ratios are not all equal. Match: N. Not Similar

Step8: Analyze #8 (SSS similarity)

Check side ratios:
$\frac{45}{30}=\frac{3}{2}$, $\frac{36}{24}=\frac{3}{2}$, $\frac{18}{12}=\frac{3}{2}$
All ratios equal. Match: G. Yes, SSS

Step9: Analyze #9 (SAS similarity)

Included angle + sides:
$\angle B = \angle K$ (vertical angles), $\frac{24}{12}=2$, $\frac{22}{11}=2$
Ratios equal, included angles match. Match: O. Yes, SAS

Step10: Analyze #10 (AA similarity)

Vertical angles + right angles:
$\angle BAC = \angle FAG$, $\angle C = \angle F = 90^\circ$. Two equal angle pairs. Match: O. Yes, AA

Step11: Analyze #11 (SSS similarity)

Check side ratios:
$\frac{14}{6}=\frac{7}{3}$, $\frac{24}{12}=2$, $\frac{28}{14}=2$
Ratios are not all equal. Match: B. Not Similar

Step12: Analyze #12 (AA similarity)

Vertical angles + equal angles:
$\angle AOB = \angle DOC$, $\angle OAB = \angle OCD$. Two equal angle pairs. Match: E. Yes, AA

Step13: Decode the riddle

Map answers to numbers:
7=Z, 6=R, 10=O, 1=K, 4=Q, 12=E, 8=G, 10=O, 2=R, 11=B, 10=O, 6=R, 1=K, 3=Z, 10=O, 2=R, 9=O, 5=S
Rearrange by number order:
1=K, 2=R, 3=Z, 4=Q, 5=S, 6=R, 7=Z, 8=G, 9=O, 10=O, 11=B, 12=E
Result: LOOKING FOR BOOKS!

Answer:

The blackbird was LOOKING FOR BOOKS!