Which method is used to prove a figure is an isosceles trapezoid?

To establish that a figure is an isosceles trapezoid, one effective method is to use slope and distance to confirm that one pair of sides are parallel and the non-parallel sides are congruent. An isosceles trapezoid is defined as a trapezoid with one pair of opposite sides parallel (the bases), while the other pair of non-parallel sides (the legs) must be equal in length.

By using the slope formula, you can determine whether the two sides claimed to be the bases are parallel; if they have the same slope, they are parallel. Then, by applying the distance formula to measure the length of the non-parallel sides, you can verify that the lengths of these sides are equal. This confirms that the figure meets the criteria for being an isosceles trapezoid, as it possesses both a pair of parallel sides and two congruent legs.

In contrast, proving two pairs of angles congruent does not directly define an isosceles trapezoid without further context. Showing that the diagonals are equal in length is a property of isosceles trapezoids but is a consequence rather than a defining characteristic. Calculating the area does not inherently confirm the