Final answer:
Jane can check the shape of a door frame corner by measuring the diagonals to ensure they are equal or use the 3-4-5 rule to confirm a right angle.
Step-by-step explanation:
Jane wants to check the shape of the corner of a door frame but does not have a tool to measure angles. To confirm that the corner is a right angle (90 degrees) without a specific measuring tool, Jane can use the mathematical principle that in a rectangle, the diagonals are equal. She can measure the diagonals of the door frame; if they are the same length, this would indicate that the frame is rectangular and the corners are right angles. Another approach is using the concept of the 3-4-5 triangle, which is a Pythagorean triple. For this, Jane would measure three segments from the corner along one edge 3 units in length, along the other edge 4 units in length, and the diagonal between the end of those two segments should be 5 units if the corner is a right angle.