We perform several consistency tests between different phases of binary black hole dynamics; the inspiral, the merger, and the ringdown on the gravitational wave events GW150914 and GW170814. To perform these tests we excise the data explicitly in the time domain to avoid any spectral leakage between the different phases using gating and inpainting method. We estimate the posterior distributions on the mass and spin of the initial black holes and the final black hole separately and independently from the different phases in frequency-domain. We also compute the initial areas of the two individual black holes and the final area from the parameters describing the remnant black hole. This facilitates a test of Hawking's black hole area theorem. We use different waveform models to quantify systematic waveform uncertainties for the area increase law with the two events. We find that these errors may lead to overstating the confidence with which the area theorem is confirmed. For example, we find > 99% agreement with the area theorem for GW150914 if a damped sinusoid consisting of a single mode is used at merger to estimate the final area. This is because this model overestimates the final mass. Including an overtone of the dominant mode decreases the confidence to-94%; using a full merger-ringdown model further decreases the confidence to-85-90%. We find that comparing the measured change in area to the expected change in area yields a more robust test, as it also captures over estimates in the change of area. We find good agreement with GR when applying this test to GW150914 and GW170814.