If quadrilateral ABCD is an isosceles trapezoid, which statements must be true? Check all that apply. (Pick more than one)
2 answers:
Answer: The correct statements are shown in option 1, 3 and 5.
Explanation:
It is given that quadrilateral ABCD is an isosceles trapezoid.
An isosceles trapezoid is a special case of trapezoid. In this trapezoid there is line of symmetry which bisects the one of the pairs of opposite sides.
From the below figure it is noticed that the line of symmetry must be a vertical line, which intersects the line BC and AD.
It is means the both sides of vertical dotted line are congruent.
From the figure we can easily noticed that BC is parallel to AD.
Since BA is the image of CD across the axis of symmetry, therefore BA is congruent to CD.
The angle CBA is the image of angle BCD across the axis of symmetry, therefore angle CBA is congruent to angle BCD.
Therefore the correction options are 1, 3 and 5.
From the figure it is noticed that the line BD is not perpendicular to AC and BE is not congruent to ED, therefore the option 2 and 4 are incorrect.
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