Short Answer 
A rhombus is a quadrilateral with all sides equal and diagonals intersecting at right angles and bisecting each other. To find lengths of segments, use Pythagoras’ theorem, applying it to given values to determine segment lengths within the rhombus.
Step 1: Understand the Properties of a Rhombus
A rhombus is a special type of quadrilateral characterized by having all four sides of equal length. It also has unique properties related to its diagonals, which are the line segments that connect opposite corners. The diagonals of a rhombus intersect at right angles and bisect each other, meaning they cut each other in half at a 90-degree angle.
Step 2: Apply Pythagoras’ Theorem
To find the lengths of the diagonals or other segments in a rhombus, you can use Pythagoras’ theorem. For example, in the rhombus TUVW where TW = 8 and WX = 5, you can set up the equation: TW¬¨‚⧠= TX¬¨‚⧠+ WX¬¨‚â§. This will allow you to calculate the length of TX by rearranging the equation and plugging in the values from the problem.
Step 3: Calculate the Lengths of Segments
Once you apply Pythagoras’ theorem, you can determine the lengths of segments in the rhombus. For instance, from the above calculation, you find TX = XV = ‚Äöao39 and WX = XU = 5. Both TX and XV are equivalent due to the property that the diagonals bisect each other. This confirms the lengths and the relationships between the segments in the rhombus.