Reduced-order template models like the Linear Inverted Pendulum (LIP) and\nSpring-Loaded Inverted Pendulum (SLIP) are widely used tools for controlling\nhigh-dimensional humanoid robots. However, connections between templates and\nwhole-body models have lacked formal underpinnings, preventing formal\nguarantees when it comes to integrated controller design. We take a small step\ntowards addressing this gap by considering the notion of approximate\nsimulation. Derived from simulation relations for discrete transition systems\nin formal methods, approximate similarity means that the outputs of two systems\ncan remain $\\epsilon$-close. In this paper, we consider the case of controlling\na balancer via planning with the LIP model. We show that the balancer\napproximately simulates the LIP and derive linear constraints that are\nsufficient conditions for maintaining ground contact. This allows for rapid\nplanning and replanning with the template model by solving a quadratic program\nthat enforces contact constraints in the full model. We demonstrate the\nefficacy of this planning and control paradigm in a simulated push recovery\nscenario for a planar 4-link balancer.\n