Q: What is the value of an isosceles trapezoid?

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Yes, an isosceles trapezoid is symmetrical.

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

No. It can be but need not be.

The base angles of an isosceles trapezoid are congruent

yes! But only an isosceles Trapezoid.

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3

No, not every trapezoid is an isosceles trapezoid.

What is 'isococeles'? Do you mean 'Isosceles'. If so , then you need to specify 'x' , be it an angle or a side length.

An isosceles trapezoid

maybe 3.5

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

It depends on what x represents, and what information you have about the trapezoid.

The diagonals of an isosceles trapezoid are equal in lengths

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.

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