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LX ≅ LZ is not true for the given rhombus WXYZ.
The correct option is (B).
the problem step by step.
1. Given Information:
- Quadrilateral WXYZ is a rhombus, but it is **not** a square.
- We need to evaluate which of the given statements is **not true** for this rhombus.
2. Statements to Evaluate:
- Let's consider each statement:
-WX ≅ YZ: In any rhombus, opposite sides are congruent. So, this statement is **true**.
- LX ≅ LZ: This refers to the diagonals of the rhombus. In a square, diagonals are congruent, but in a general rhombus, they aren't necessarily so. Therefore, this statement is **not true** for a rhombus that isn't also a square.
- WY ⊥ XZ: The diagonals of any rhombus are perpendicular to each other. So, this statement is **true**.
- WY ≅ XZ: In any rhombus, diagonals bisect each other but aren't necessarily congruent (they are in a square). So this statement is also true.
- The second option (LX ≅ LZ) isn't typically correct for a general rhombus that isn't also a square.
Therefore, the answer is that LX ≅ LZ is not true for the given rhombus WXYZ.
Remember, this analysis assumes that WXYZ is a rhombus that is not a square. If it were a square, all the statements would be true.
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