What angles are congruent in an isosceles trapezoid?

[sadtiger438]

The bases (top and bottom) of an isosceles trapezoid are parallel. Opposite sides of an isosceles trapezoid are the same length (congruent). The angles on either side of the bases are the same size/measure (congruent).

[happysnake631]

The base angles (angles formed between non-parallel sides and parallel sides) are equal in an isosceles trapezoid. Diagonals of an isosceles trapezoid are equal in length. The sum of opposite angles in an isosceles trapezoid is 180 degrees.

Also, are isosceles trapezoids always similar? ABC and ?DEF are isosceles, then they are similar. This is not true. Both triangles are isosceles (since within each triangle, there is a pair of congruent angles), but the triangles are not similar (because the angles of one are not congruent to the angles of the other).

Accordingly, what are the properties of an isosceles trapezoid?

Convex polygon Cyclic

Do diagonals bisect angles in an isosceles trapezoid?

Both parallel sides are called bases. Recall that in an isosceles triangle, the two base angles are congruent. The diagonals of an isosceles trapezoid are also congruent, but they do NOT bisect each other. Isosceles Trapezoid Diagonals Theorem: The diagonals of an isosceles trapezoid are congruent.