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Q: What is the meaning of an isosceles trapezoid?

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No, not every trapezoid is an isosceles trapezoid.

Yes, an isosceles trapezoid is symmetrical.

how is an isoscelels trapezoid related to a isosceles triangle

In an isosceles triangle and an isosceles trapezoid, both base angles are congruent

The diagonals of an isosceles trapezoid are equal in lengths

No. It can be but need not be.

If you extend the two legs of an isosceles trapezoid until they intersect, you get an isosceles triangle.

If the two sides which are not parallel have equal lengths, then the trapezoid is called an isosceles trapezoid (standard trapezoid has unequal sides). The base angles in an isosceles trapezoid are equal in measurement, also I know that a trapezoid with two nonparallel sides the same length is called an isosceles trapezoid.

An isosceles trapezoid

A ISOSCELES TRAPEZOID HAS ONE LINE OF SYMMETRY.....

The base angles are congruent in an isosceles trapezoid

An isosceles triangle and a isosceles trapezoid.

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