Math Problem Statement

Select all the true statements about trapezoids and their properties.

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:
    Median=Base1+Base22\text{Median} = \frac{\text{Base}_1 + \text{Base}_2}{2}

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:

  1. What distinguishes an isosceles trapezoid from a general trapezoid?
  2. How do you calculate the length of the median of a trapezoid?
  3. Can a trapezoid have both pairs of sides parallel? Why or why not?
  4. What properties do the diagonals of an isosceles trapezoid have?
  5. 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