This study addresses the problem of geometric consistency between displayed images and real scenes in augmented reality using a video see-through hand-held display or tablet. To solve this problem, we present approximated user-perspective images rendered by homography transformation of camera images. Homography approximation has major advantages not only in terms of computational costs, but also in the quality of image rendering. However, it can lead to an inconsistency between the real image and virtual objects. This study also introduces a variety of rendering methods for virtual objects and discusses the differences between them. We implemented two prototypes and designed three types of user studies on matching tasks between real scenes and displayed images. We have confirmed that the proposed method works in real time on an off-the-shelf tablet. Our pilot tests show the potential to improve users's visibility, even in real environments, by using our method.