Final answer:
The Senate is responsible for approving Presidential appointments to high government positions. This follows the 'Advice and Consent' provision stated in Article II, Section 2 of the Constitution.
Step-by-step explanation:
The house of Congress that must approve Presidential appointments to high government positions is the Senate. According to Article II, Section 2 of the Constitution, the President nominates individuals for high-level positions, including federal judges, ambassadors, and various other official roles. These appointments require the 'Advice and Consent' of the Senate, which means that a majority of Senators must approve the Presidential appointees. This process involves potential hearings and a vote. While most appointees are confirmed in a routine manner, there are instances when the Senate may choose not to schedule a vote or reject a nominee, especially if there are concerns or controversy surrounding the appointment.