1. Two triangles are shown with markings indicating equal parts. In $\triangle ABC$ and $\triangle DEF$, $\angle A$ is marked congruent to $\angle D$ (one arc), and $\angle B$ is marked congruent to $\angle E$ (two arcs). The side between those angles, $AB$, has one tick mark, and the corresponding side $DE$ also has one tick mark.
Which congruence criterion applies (SSS, SAS, ASA, AAS)?
2. Two triangles are shown. In $\triangle ABC$, $AB=6$, $AC=9$, $BC=12$. In $\triangle DEF$, $DE=4$, $DF=6$, $EF=8$. What is the scale factor from $\triangle ABC$ to $\triangle DEF$ (i.e., multiply lengths in $\triangle ABC$ by what number to get corresponding lengths in $\triangle DEF$)?
3. In $\triangle ABC$ and $\triangle DEF$, $\angle A\cong\angle D$, $\angle B\cong\angle E$, and the side between them is equal: $AB=DE=7$. Which congruence criterion applies (SSS, SAS, ASA, AAS)?
4. Triangles $\triangle JKL$ and $\triangle MNO$ are similar. Corresponding sides are $JK \leftrightarrow MN$, $KL \leftrightarrow NO$, and $JL \leftrightarrow MO$. If $JK=8$, $KL=10$, $JL=12$, and $MN=12$, what is the length of $NO$?
5. Triangles $\triangle GHI$ and $\triangle JKL$ are similar by AA with correspondence $G\leftrightarrow J$, $H\leftrightarrow K$, $I\leftrightarrow L$. If $GH=12$, $JK=8$, and $HI=15$, what is the length of the corresponding side $KL$?
6. Triangles $\triangle PQR$ and $\triangle STU$ are similar by AA. Angle $\angle P$ corresponds to $\angle S$, and $\angle Q$ corresponds to $\angle T$. If $PQ=6$ and the corresponding side $ST=9$, what is the scale factor from $\triangle PQR$ to $\triangle STU$?
7. In triangle ABC and triangle XYZ, if $\text{angle } A = \text{angle } X$ and $\text{angle } B = \text{angle } Y$, are the triangles similar?
8. For triangles $\triangle XYZ$ and $\triangle ABC$, $\triangle XYZ$ has angles $X = 45^\text{o}$, $Y = 45^\text{o}$, and $\triangle ABC$ has angles $A = 45^\text{o}$, $B = 45^\text{o}$. Are the triangles similar?
9. Two triangles, $\triangle GHI$ and $\triangle JKL$, $\triangle GHI$ has angles $G = 60^\text{o}$, $H = 60^\text{o}$, and $\triangle JKL$ has angles $J = 60^\text{o}$, $K = 60^\text{o}$. Are the triangles similar?
10. Triangles $\triangle ABC$ and $\triangle DEF$ are shown. The side markings indicate $AB \cong DE$ (one tick) and $BC \cong EF$ (two ticks). Also, $\angle B \cong \angle E$ is marked, and it is the included angle between the tick-marked sides. Which congruence criterion applies?
11. Two triangles are shown. In $\triangle ABC$, $AB\=6$, $BC\=9$, $AC\=12$. In $\triangle DEF$, $DE\=4$, $EF\=6$, $DF\=8$. Are the triangles similar? If so, why?
12. Which triangles are similar if $\triangle ABC$ has sides $6, 8, 10$ and $\triangle DEF$ has sides $9, 12, 15$?
13. If $\triangle XYZ \thicksim \triangle VWU$ with $XZ = 6$ and $VW = 12$, what is the ratio of $YZ$ to $WU$?
14. Which triangles are similar if $\triangle ABC$ has sides $5, 12, 13$ and $\triangle DEF$ has sides $10, 24, 26$?
15. If $\triangle LMN \thicksim \triangle OPQ$ with $LM = 6$ and $OP = 18$, what is the ratio of $MN$ to $PQ$?
16. Triangles $\triangle ABC$ and $\triangle DEF$ are shown with side lengths: $AB\=9$, $BC\=12$, $AC\=15$ and $DE\=6$, $EF\=8$, $DF\=10$.
What is the scale factor from $\triangle DEF$ to $\triangle ABC$?
17. Two triangles are shown. In $\triangle RST$, angles at $R$ and $S$ are marked with one arc and two arcs, respectively. In $\triangle VWX$, angles at $V$ and $W$ are marked with one arc and two arcs, respectively.
Which congruence/similarity criterion applies to conclude the triangles are similar?
18. Two triangles are drawn with the following markings: In $\triangle ABC$ and $\triangle DEF$, sides $AB$ and $DE$ each have one tick mark, sides $AC$ and $DF$ each have two tick marks, and the included angles $\angle A$ and $\angle D$ are marked equal (single arc). The labeled lengths are $AB=5$, $AC=7$, $DE=5$, and $DF=7$.
Which congruence criterion applies to conclude $\triangle ABC \cong \triangle DEF$?
19. Two triangles are shown with angle markings. In $\triangle PQR$, $\angle P$ has one arc and $\angle Q$ has two arcs. In $\triangle STU$, $\angle S$ has one arc and $\angle T$ has two arcs. Side lengths are not needed.
Are the triangles similar? If so, why?
20. Two triangles are shown with side tick marks and one angle mark. In $\triangle JKL$ and $\triangle MNO$, $JK$ and $MN$ each have one tick mark, $JL$ and $MO$ each have two tick marks, and the included angles $\angle J$ and $\angle M$ are each marked with a single arc.
Which congruence criterion applies (SSS, SAS, ASA, AAS)?
21. Two triangles have $\angle A \cong \angle D$, $\angle C \cong \angle F$, and the side between those angles satisfies $AC=7$ and $DF=7$. Which congruence criterion applies?
22. Two triangles have side lengths $AB=6$, $BC=8$, $AC=10$ and $DE=9$, $EF=12$, $DF=15$. Which statement is true about their relationship?
23. Triangle DEF is similar to triangle GHI. If $DE = 6$, $EF = 8$, and $GH = 12$, what is the length of $HI$?
24. Two triangles, $\triangle JKL$ and $\triangle MNO$, are congruent. If $JK = 8$, $KL = 15$, $JL = 17$, what is the length of $MN$ if $MN$ corresponds to $JK$?
25. Which congruence criterion applies to triangles MNO and PQR if $MN = PQ$, $\text{angle } N = \text{angle } Q$, and $NO = QR$?
26. Are the triangles ABC and DEF similar if $\text{angle } A = \text{angle } D$, $\text{angle } B = \text{angle } E$, and $AB = DE$?
27. Two triangles, $\triangle ABC$ and $\triangle DEF$, are shown with $\triangle ABC \text{ having sides } AB = 6, BC = 8, \text{ and } AC = 10$. $\triangle DEF \text{ has sides } DE = 9, EF = 12, \text{ and } DF = 15$. Are the triangles similar? If so, why?
28. Triangles WXY and ZAB are shown to be similar by which criterion if $\text{angle } W = \text{angle } Z$ and $\text{angle } X = \text{angle } A$?
29. Two triangles are shown with side lengths. $\triangle ABC$ has sides $AB\=4$, $BC\=7$, $AC\=9$. $\triangle DEF$ has sides $DE\=8$, $EF\=14$, $DF\=18$. Which statement is true? 
30. Two triangles $\triangle PQR$ and $\triangle STU$ are shown. The sides with one tick mark are $PQ\=4$ and $ST\=6$, and the sides with two tick marks are $PR\=10$ and $SU\=15$. The included angles $\angle P$ and $\angle S$ are marked congruent with matching arcs. Are the triangles similar? If so, why?
31. Triangles $\triangle ABC$ and $\triangle DEF$ are shown. $\angle A \cong \angle D$ and $\angle B \cong \angle E$ are marked. Side $AB\=10$ and $DE\=5$. What is the scale factor from $\triangle ABC$ to $\triangle DEF$?
32. Triangles $\triangle ABC$ and $\triangle DEF$ are shown. Angles $\angle A$ and $\angle D$ are marked congruent (one arc), and angles $\angle C$ and $\angle F$ are marked congruent (two arcs). No side lengths are needed. Which statement is true?
33. Two triangles are shown: $\triangle ABC$ has $AB\=8$, $BC\=6$, and $AC\=10$. $\triangle DEF$ has $DE\=12$, $EF\=9$, and $DF\=15$. No angles are marked. Are the triangles similar? If so, why?
34. Two triangles have the following marked information: $\angle A \cong \angle D$, $\angle B \cong \angle E$, and a non-included side $AC=13$ equals $DF=13$. Which congruence criterion applies?
35. In $\triangle ABC$, the side lengths are $AB=6$, $AC=8$, and $BC=10$. In $\triangle DEF$, the side lengths are $DE=9$, $DF=12$, and $EF=15$. Which triangles are similar?
36. In similar triangles $\triangle ABC \sim \triangle DEF$, the correspondence is $A\leftrightarrow D$, $B\leftrightarrow E$, $C\leftrightarrow F$. If $AB=8$, $DE=12$, and $BC=10$, what is $EF$?
37. In $\triangle ABC$, $AB=7$, $AC=9$, and $BC=12$. In $\triangle DEF$, $DE=14$, $DF=18$, and $EF=20$. Are the triangles similar? If so, why?
38. Triangles $\triangle RST$ and $\triangle XYZ$ are similar. The scale factor from $\triangle RST$ to $\triangle XYZ$ is $\dfrac{3}{2}$. If $RS=10$ and $ST=14$, what is the perimeter of $\triangle XYZ$ if the perimeter of $\triangle RST$ is $36$?
39. Triangles $\triangle ABC$ and $\triangle DEF$ are similar with correspondence $A\leftrightarrow D$, $B\leftrightarrow E$, $C\leftrightarrow F$. If $AB=9$, $BC=12$, $AC=15$, and $DE=6$, what is the length of $EF$?
40. Two triangles are shown. In $\triangle WXY$, $WX=8$ and $WY=12$, and the included angle $\angle W$ is marked as $50^\circ$. In $\triangle ZUV$, $ZU=12$ and $ZV=18$, and the included angle $\angle Z$ is also marked as $50^\circ$.
Are the triangles similar? If so, why?
41. Triangles $\triangle PQR$ and $\triangle STU$ are shown with side lengths $PQ=4$, $QR=6$, $PR=8$ and $ST=6$, $TU=9$, $SU=12$.
What is the scale factor from $\triangle PQR$ to $\triangle STU$ (i.e., multiply lengths in $\triangle PQR$ by what number to get corresponding lengths in $\triangle STU$)?
42. Two triangles have side lengths $\triangle ABC$: $AB=6$, $BC=10$, $AC=12$ and $\triangle DEF$: $DE=3$, $EF=5$, $DF=6$.
Are the triangles similar? If so, why?
43. Triangles $\triangle GHI$ and $\triangle JKL$ are shown. In $\triangle GHI$, $GH=9$, $HI=12$, and $GI=15$. In $\triangle JKL$, $JK=6$, $KL=8$, and $JL=10$.
What is the scale factor from $\triangle JKL$ to $\triangle GHI$?
44. Which triangles are similar if $\triangle RST$ has sides $7, 24, 25$ and $\triangle ABC$ has sides $14, 48, 50$?
45. Triangles $\triangle MNO$ and $\triangle RST$ have $MN=6$, $NO=9$, $MO=12$ and $RS=4$, $ST=6$, $RT=8$. What is the scale factor from $\triangle RST$ to $\triangle MNO$ (using corresponding sides $RS\leftrightarrow MN$, $ST\leftrightarrow NO$, $RT\leftrightarrow MO$)?
46. Which congruence criterion applies to triangles ABC and DEF if $AB = DE$, $\text{angle } B = \text{angle } E$, and $BC = EF$?
47. Which congruence criterion applies to $\triangle GHI$ and $\triangle JKL$ if $GH = JK$, $\text{angle } G = \text{angle } J$, and $HI = KL$?
48. Are the triangles similar? In $\triangle RST$, $RS=6$, $ST=9$, and $RT=12$. In $\triangle XYZ$, $XY=8$, $YZ=12$, and $XZ=16$.
49. Two triangles, $\triangle KLM$ and $\triangle NOP$, have $\triangle KLM \text{ with angles } K = 40^\text{o}, L = 60^\text{o}$. $\triangle NOP \text{ has angles } N = 40^\text{o}, O = 80^\text{o}$. Are these triangles congruent?
50. For triangles $\triangle ABC$ and $\triangle DEF$, $\triangle ABC$ has angles $A = 70^\text{o}$, $B = 50^\text{o}$, and $\triangle DEF$ has angles $D = 70^\text{o}$, $E = 50^\text{o}$. Which criterion confirms their similarity?
51. Two triangles $\triangle ABC$ and $\triangle DEF$ are shown. $AB\=5$, $AC\=7$, and $BC\=8$. In the other triangle, $DE\=10$, $DF\=14$, and $EF\=16$. Which statement is correct?
52. Triangles $\triangle ABC$ and $\triangle DEF$ are shown. $\angle A \cong \angle D$ and $\angle B \cong \angle E$ are marked. Also, the side $BC$ is marked congruent to $EF$ (one tick), but it is not the included side between the marked angles. Which congruence criterion applies?
53. In $\triangle QRS$, $QR=9$, $RS=12$, and $QS=15$. In $\triangle TUV$, $TU=3$, $UV=4$, and $TV=5$. Which triangles are similar?
54. Two triangles are shown with side lengths: $\triangle ABC$ has $AB=5$, $BC=7$, $AC=9$. $\triangle DEF$ has $DE=5$, $EF=7$, $DF=9$. Which congruence criterion applies (SSS, SAS, ASA, AAS)?
55. Triangles $\triangle ABC$ and $\triangle DEF$ are similar with correspondence $A\leftrightarrow D$, $B\leftrightarrow E$, $C\leftrightarrow F$. If $AB=5$ and $DE=10$, and $BC=7$, what is the length of side $EF$ using similarity?
56. Two triangles have these measurements: In $\triangle ABC$, $AB=6$, $AC=8$, and the included angle $\angle A=50^\circ$. In $\triangle DEF$, $DE=9$, $DF=12$, and the included angle $\angle D=50^\circ$. Are the triangles similar? If so, why?
57. If $\triangle XYZ \thicksim \triangle ABC$ with $XY = 5$ and $AB = 15$, what is the ratio of $YZ$ to $BC$?
58. A person who is 6 feet tall casts a 4-foot shadow on the ground. At the same time, a nearby tree casts a 20-foot shadow. Assuming the ground is flat and both the person and tree are perpendicular to the ground, what is the height, in feet, of the tree?
59. At 3:00 PM, a flagpole casts a 24-foot shadow and a 6.0-foot-tall man casts a 4.0-foot shadow. What is the height, in feet, of the flagpole?
60. In $\triangle ABC$ and $\triangle DEF$, the triangles are similar such that $A$ corresponds to $D$, $B$ corresponds to $E$, and $C$ corresponds to $F$. If $AB = 6$, $BC = 8$, $AC = 10$, and $DE = 9$, what is the length of $\overline{DF}$?
61. Which triangles are similar if $\triangle WXY$ has angles $W = 60^\text{o}$, $X = 50^\text{o}$, and $\triangle ZUV$ has angles $Z = 60^\text{o}$, $U = 50^\text{o}$?
62. In triangles $\triangle ABC$ and $\triangle DEF$, $\triangle ABC$ has sides $AB = 4$, $BC = 3$, $CA = 5$. $\triangle DEF$ has sides $DE = 8$, $EF = 6$, $FD = 10$. Are these triangles similar?
63. For $\triangle KLM$ and $\triangle OPQ$, $\triangle KLM$ has sides $KL = 5$, $LM = 12$, $KM = 13$. $\triangle OPQ$ has sides $OP = 10$, $PQ = 24$, $OQ = 26$. What is the scale factor from $\triangle KLM$ to $\triangle OPQ$?
64. Given $\triangle RST$ with sides $RS = 7$, $ST = 24$, $RT = 25$, and $\triangle XYZ$ with sides $XY = 14$, $YZ = 48$, and $XZ = 50$. What is the scale factor from $\triangle RST$ to $\triangle XYZ$?
65. For triangles $\triangle PQR$ and $\triangle STU$, $\triangle PQR$ has sides $PQ = 8$, $QR = 15$, $RP = 17$. $\triangle STU$ has sides $ST = 16$, $TU = 30$, $US = 34$. What is the scale factor from $\triangle PQR$ to $\triangle STU$?
66. In triangles $\triangle MNO$ and $\triangle PQR$, $\triangle MNO$ has sides $MN = 9$, $NO = 12$, $OM = 15$. $\triangle PQR$ has sides $PQ = 18$, $QR = 24$, $RP = 30$. What is the scale factor from $\triangle MNO$ to $\triangle PQR$?
67. Given $\triangle GHI \text{ with sides } GH = 5, HI = 12, \text{ and } IG = 13$, and $\triangle JKL \text{ with sides } JK = 10, KL = 24, \text{ and } LJ = 26$. What is the scale factor from $\triangle GHI$ to $\triangle JKL$?
68. A 6-foot tall person casts a shadow that is 4 feet long. At the same time, a nearby flagpole casts a shadow that is 18 feet long. What is the height, in feet, of the flagpole?
69. In $\triangle ABC$ and $\triangle DEF$, $AB=9$, $AC=12$, and the included angle $\angle A$ equals the included angle $\angle D$. Also, $DE=12$ and $DF=16$. Are the triangles similar? If so, why?
70. In $\triangle ABC$ and $\triangle DEF$, $\angle A \cong \angle D$ and $\angle B \cong \angle E$. Also, $AB=10$ and $DE=15$. What is the scale factor from $\triangle ABC$ to $\triangle DEF$?
71. In similar triangles $\triangle ABC \sim \triangle DEF$ with correspondence $A\leftrightarrow D$, $B\leftrightarrow E$, $C\leftrightarrow F$, $AC=12$ and $DF=18$. If $BC=11$, what is $EF$?
72. $$\triangle PQR$ has sides $PQ=5$, $QR=7$, $PR=9$. $\triangle XYZ$ has sides $XY=10$, $YZ=14$, $XZ=18$. Are the triangles similar? If so, why?
73. Two triangles are shown with side lengths marked: in $\triangle PQR$, $PQ\=4$, $QR\=6$, $PR\=8$. In $\triangle STU$, $ST\=6$, $TU\=9$, $SU\=12$.
Are the triangles similar? If so, why?
74. Two triangles are shown with side lengths. Triangle $\triangle GHI$ has $GH=7$, $HI=9$, and $GI=12$. Triangle $\triangle JKL$ has $JK=14$, $KL=18$, and $JL=20$.
Are the triangles similar? If so, why?
75. In similar triangles LMN and OPQ, if the scale factor from LMN to OPQ is $3:2$ and $LM = 9$, what is the length of $OP$?
76. Triangles KLM and NOP are similar with a scale factor of $4:3$. If $KL = 12$, what is $NO$?
77. In $\triangle XYZ$ and $\triangle ABC$, $\triangle XYZ$ has angles $X = 90^\text{o}$, $Y = 45^\text{o}$, and $\triangle ABC$ has angles $A = 90^\text{o}$, $B = 45^\text{o}$. Are the triangles similar?
78. Two triangles are drawn. In $\triangle LMN$ and $\triangle QRS$, the following are marked: $\angle L \cong \angle Q$ (one arc), $\angle M \cong \angle R$ (two arcs), and the side between them is marked equal: $LM \cong QR$ (single tick). The length shown is $LM=11$.
Which congruence criterion applies to conclude $\triangle LMN \cong \triangle QRS$?
79. Two triangles, $\triangle DEF$ and $\triangle GHI$, are congruent. If $DE = 5$, $EF = 12$, $DF = 13$, what is the length of $GH$ if $GH$ corresponds to $DE$?
80. Two triangles have side lengths $8$, $10$, $12$ and $12$, $15$, $18$. Which triangles are similar (using the given side lengths only)?
81. A person who is 6 feet tall casts a 4-foot shadow on the ground. At the same time, a nearby tree casts a 20-foot shadow. Assuming the ground is flat and both the person and tree are perpendicular to the ground, what is the height, in feet, of the tree?