Isosceles Trapezoid Diagonals: Do They Have Equal Length and Intersect?

To determine the properties of an isosceles trapezoid's diagonals, follow these steps:

• Step 1: Define an isosceles trapezoid.

An isosceles trapezoid is a quadrilateral with one pair of opposite sides that are parallel (bases), and the non-parallel sides (legs) are equal in length.

• Step 2: Analyze the properties of the diagonals in an isosceles trapezoid.

One fundamental property of isosceles trapezoids is that their diagonals are congruent. This means that the lengths of the two diagonals are equal. This property arises because the legs are equal, and consequently, the angles at the bases also exhibit special symmetry, leading to equal diagonals.

• Step 3: Determine if the diagonals intersect.

In any convex quadrilateral, which includes an isosceles trapezoid, the diagonals will intersect each other at a point inside the quadrilateral. This follows from the definition of a convex shape, where diagonals cross each other.

Hence, it follows that not only are the diagonals of an isosceles trapezoid equal in length, but they also intersect each other.

Therefore, the correct answer to the question is Yes.