Check if two points are symmetrics/asymmetric

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The discussion focuses on determining the symmetry of freehand-drawn shapes in an Android app designed for children. The user provides two sets of coordinates representing shapes they consider symmetric, despite differences in inclination and length. A key point raised is the need for a flexible definition of symmetry that accommodates variations in shape. The conversation highlights the challenge of comparing non-standard geometric figures and the necessity for a clear definition of symmetry in this context.

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I'm working on an Android app which let's a group of child to draw whatever they want in a specific area. I need to check if the lines and figure that they draw are symmetric. The problem is that since the app is designed to let them draw freehand, I don't know how to compare the lines by considering a certain flexibility. For example, I would consider symmetric these two "triangles" in the image: https://imgur.com/a/SH9dYPm even if they have not the same inclination and the same length. Do you have any suggestion? These are the points of the two shapes, do you notice any constant or something similar I can use to find what I need?
Triangle on the top:
HTML: 
1303.9062, 245.88171
1306.9531, 239.48767
1309.055, 234.89392
1309.9219, 231.82782
1312.2241, 231.00659
1312.8906, 228.64291
1312.8906, 226.54477
1315.9375, 227.98535
1315.9375, 231.00659
1319.2817, 236.99414
1319.9219, 243.00916
1322.1042, 244.02539
1322.8906, 248.47485
1322.8906, 251.52356
1322.8906, 255.54462
1324.9263, 256.98926
1325.9375, 260.74615
1325.9375, 265.4226
1325.9375, 267.45148
1325.9375, 269.0193
1330.1698, 269.0193
1328.9062, 275.0343
1328.9062, 275.9956
1328.9062, 279.01685
1328.9062, 281.98315
1331.9531, 285.0044
1331.9531, 285.0044
Triangle in the bottom:

HTML: 
1133.9062, 950.9956
1133.9062, 955.37256
1136.1552, 959.9429
1136.9531, 965.0901
1138.6583, 968.71606
1139.9219, 972.3617
1142.586, 976.9783
1143.9062, 982.42285
1146.608, 985.6449
1146.9531, 990.5189
1149.9219, 999.83105
1149.9219, 1002.55286
1153.7056, 1005.82275
1152.8906, 1010.1306
1154.862, 1011.9697
1155.9375, 1016.5016
1155.9375, 1018.0122
1155.9375, 1020.9785
1155.9375, 1024.9885
1159.9219, 1024.9885
1163.43, 1017.47314
1162.8906, 1013.48035
1165.9375, 1008.792
1167.0302, 1000.8804
1168.9062, 995.6416
1171.9531, 990.8357
1175.2189, 986.532
1175.9375, 981.4552
1178.9062, 975.46765
1181.9531, 970.21094
1181.9531, 966.84827
1186.4062, 966.9807
1184.9219, 962.5906
1184.9219, 960.99316
1187.8906, 960.99316
1187.8906, 956.98315
1187.8906, 956.98315
 
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I would consider symmetric these two "triangles" in the image: ​

https://imgur.com/a/SH9dYPm


First I see NO triangles in that, just two curves. And since you say that, exactly what is your definition of "symmetric"?​

 
Also, I plotted that first list of points to get:
View attachment 9315
I can't make any sense out of what you want. And I don't see any triangles there.
 

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