therefore judgeing by the em diagram the yak is an energy fighter and should avoid angle fighting.
That depends on what adversary aircraft you are referring to. A fighter only becomes the Angles or Energy fighter in comparison to a specific enemy aircraft and for specific aircraft configuration. This is easier to see if you overlay EM diagrams. Here are two overlays for the Yak9U one with the Spit16 and the other with the P-51D. In the first case, against the Spitfire you would be right, the Yak would need to keep the fight fast, employ energy tactics. Also, looking at that diagram it can be seen that the Spitfire has a Ps advantage at all speeds below 300mph so as the Yak driver I would want to engage with a significant energy advantage, use energy tactics, and break off the engagement before the advantage was gone, and use my small speed advantage to bug out.
Against the P-51D though, the situation is different. Inspection of the diagram below shows that the Yak9U is the Angles Fighter. If you can force the P-51D to engage you will have a significant sustained and instantaneous turning advantage.

However, that is configuration and altitude specific, so a heavy Yak v a light P-51D can make a difference. For example, the diagram below shows what would happen if a Yak9U with 100% internal fuel met a P-51D that was down to 10% internal fuel.

Here you can see the situation is very different, a slight instantaneous advantage to the Yak9U, but a clear sustained advantage to the P-51D. In this situation the the higher Ps for the P-51D would mean that the Yak would slow down more quickly, which combined with its slightly better instantaneous values would give it an advantage in the one circle fight, say a scissors, while the P-51D would have an advantage in a two circle fight, say a protracted Lufbery. However, with the margins as close as this, the outcome is more likely to be determined by other factors, such as pilot skill.
Lastly, you will notice how the corner velocity is dependant on aircraft weight, for example in the last EM diagram the heavy Yak9U has a corner velocity much closer to the 250mph value suggested earlier.
Hope that helps.
Badboy