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asdf1
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what does a triangle have to do with triangle inequality, and what does a paralllelogram have to do with parallelogram equality?
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asdf1 said:i'm still confused:
"triangle inequality is the theorem stating that for any triangle, the measure of a given side must be less than the sum of the other two sides but greater than the difference between the two sides."
yet "|x+y| ≤ |x|+|y| " shouldn't mean "|z|≤ |x|+|y| "?
The Triangle Inequality Theorem states that the sum of any two sides of a triangle must be greater than the length of the third side. In other words, the longest side of a triangle must be shorter than the sum of the other two sides.
The Triangle Inequality Theorem is used to determine if three given side lengths can form a valid triangle. If the theorem is not satisfied, then the given side lengths cannot form a triangle.
The Parallelogram Equality Theorem states that opposite sides of a parallelogram are congruent, and opposite angles are also congruent. This means that a parallelogram has two pairs of parallel sides and two pairs of congruent angles.
The Parallelogram Equality Theorem is used to prove that a given quadrilateral is a parallelogram. By showing that opposite sides are congruent and opposite angles are congruent, we can conclude that the figure is indeed a parallelogram.
Yes, these two theorems can be used together to determine if a given figure is a parallelogram. If the Triangle Inequality Theorem is satisfied for all three pairs of sides and the Parallelogram Equality Theorem is satisfied for opposite sides and angles, then the figure is a parallelogram.