This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

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Answer
Square
Step 1: Path with 4 right angles = yes and all sides same length = yes.
Square
Step 2: Path with 4 right angles = yes and all sides same length = no.
Rectangle
Step 3: Path with 4 right angles = no, opposite angles equal = yes, and all sides same length = yes.
Rhombus
Step 4: Path with 4 right angles = no, opposite angles equal = yes, and all sides same length = no.
Parallelogram
Step 5: Path with 4 right angles = no, opposite angles equal = no, and two pairs of adjacent sides equal length = yes.
Kite
Step 6: Path with 4 right angles = no, opposite angles equal = no, and two pairs of adjacent sides equal length = no.
Trapezoid
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Path with 4 right angles = yes and all sides same length = yes. Square Square Step 2: Path with 4 right angles = yes and all sides same length = no.
This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.