Math Problem Statement
Solution
Let's evaluate each statement in the problem to determine which are true.
A. The legs of an isosceles trapezoid are parallel.
- False. In an isosceles trapezoid, the legs (non-parallel sides) are congruent but not parallel. The bases are the parallel sides.
B. A trapezoid is a quadrilateral with at least one pair of parallel sides.
- True. This is the definition of a trapezoid: a quadrilateral with at least one pair of parallel sides.
C. A trapezoid is a quadrilateral with at least one pair of perpendicular sides.
- False. While a trapezoid can have perpendicular sides (e.g., a right trapezoid), this is not a defining property of all trapezoids.
D. The diagonals of an isosceles trapezoid may or may not be congruent to each other.
- False. In an isosceles trapezoid, the diagonals are always congruent.
E. The median of a trapezoid is parallel to the bases and half the sum of the lengths of the bases.
- True. The median (or midsegment) of a trapezoid is always parallel to the bases, and its length is given by the formula:
Final Answer:
The true statements are B and E.
Would you like a detailed explanation of any specific part?
Here are 5 related questions to deepen understanding:
- What distinguishes an isosceles trapezoid from a general trapezoid?
- How do you calculate the length of the median of a trapezoid?
- Can a trapezoid have both pairs of sides parallel? Why or why not?
- What properties do the diagonals of an isosceles trapezoid have?
- How do you identify perpendicular sides in quadrilaterals like trapezoids?
Tip: Always verify the definitions and properties of shapes like trapezoids before solving geometry problems!
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Math Problem Analysis
Mathematical Concepts
Geometry
Properties of trapezoids
Isosceles trapezoids
Formulas
Median of a trapezoid = (Base1 + Base2) / 2
Theorems
Definition of a trapezoid
Properties of isosceles trapezoids
Parallel and congruent properties of trapezoids
Suitable Grade Level
Grades 9-10
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