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How do you prove the diagonal lines in a parallelogram is not a rhombus?
Because the diagonals of a rhombus intersect each other at 90 degrees whereas in a parallelogram they don't
How would you prove that an inequality does have the same solution that an equation would have?
If you're given the inequality and the equation, then the way to prove that they have the same solution is to solve each one and show that the solutions are the same number. Don't strain yourself, though. An inequality and an equation never have the same solution.
What are not is efficient to prove that a quadrilateral is a parallelogram?
A parallelogram is a quadrilateral because it has 4 sides and all quadrilaterals have 4 sides such as a square, a rectangle, a rhombus ... etc
How can you used a triangle to prove quadrilateral is a parallelogram?
A quadrilateral, in general, is not a parallelogram. If it is a parallelogram then you will have some additional information about its sides and angles. If you do not have such information it is not possible to prove that it is a parallelogram. Draw a diagonal which will divide the quadrilateral into two triangles and use the additional information that you have to show that the triangles are congruent. This can then be used to show equality of sides or of angles: the latter can then be used to show that sides are parallel. Note that the choice of which diagonal may influence how (if at all) you proceed.
What does a rhombus have to have to prove that it is a rhombus?
a parallelogram with opposite equal acute angles, opposite equal obtuse angles, and four equal sides.
