Deep learning performance on classifying simple geometric figures
A CNN network should easily achieve close to 100% accuracy on this task. Few aspects make this task easier :


Clean High-contrast images generated from program 
Only 1 shape per image 
Given few images of a shape, libraries can generate thousands of training samples automatically with various transformations like rotations / scaling / flip 
Within few layers network should identify edge-detection patterns for vertices and learn the 3 vertices = triangle and so on 


For example, this code can generate training examples based on few input images : 

https://keras.io/preprocessing/image/

datagen = ImageDataGenerator(
    featurewise_center=True,
    featurewise_std_normalization=True,
    rotation_range=20,
    width_shift_range=0.2,
    height_shift_range=0.2,
    horizontal_flip=True)


Few articles :

https://www.researchgate.net/publication/312328148_Binary_shape_classification_using_Convolutional_Neural_Networks

https://towardsdatascience.com/object-detection-with-neural-networks-a4e2c46b4491