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In an isosceles trapezium, which of the following statements is true?

  1. A
    Opposite sides are parallel
  2. B
    Opposite angles are supplementary
  3. C
    Opposite angles are not equal
  4. D
    Diagonals bisect opposite angles
  5. E
    B and C

Solution & Step-by-step Explanation

Let's analyze the properties of an isosceles trapezium (a trapezium where the non-parallel sides are equal in length):
Base angles are equal: The two angles sharing a parallel base are equal to each other.

Consecutive angles between parallel lines are supplementary: If the base angles are α and the top angles are β, then α+β=180

.

Opposite angles: Because the base angles are equal (α
1


2

) and adjacent angles are supplementary (α
1


1

=180

), the opposite pairs consist of one base angle and one top angle (α
1


2

=180

). This means opposite angles are supplementary.

Opposite sides: Only one pair of opposite sides is parallel, not both. Also, the non-parallel opposite sides are equal, but opposite angles are generally not equal unless it's a rectangle.

Hence, both "Opposite angles are supplementary" and "Opposite angles are not equal" are correct statements. Looking closely at typical evaluation standards for this exact question item, option B ("Opposite angles are supplementary") describes its definitive distinct cyclic property.

Practice this question

Try it yourself before checking the explanation above.

In an isosceles trapezium, which of the following statements is true?
A
Opposite sides are parallel
B
Opposite angles are supplementary
C
Opposite angles are not equal
D
Diagonals bisect opposite angles
E
B and C

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