Question

1. on a rectangle, how do you know that the diagonals are the same length? 2. creators themselves with the artists make a picture.

Explanation:

Step1: Recall rectangle properties

A rectangle is a parallelogram with four right - angles.

Step2: Use congruent triangles

Let the rectangle be \(ABCD\) with diagonals \(AC\) and \(BD\). In \(\triangle ABC\) and \(\triangle DCB\), \(AB = DC\) (opposite sides of a rectangle are equal), \(\angle ABC=\angle DCB = 90^{\circ}\), and \(BC=CB\) (common side). By the Side - Angle - Side (SAS) congruence criterion, \(\triangle ABC\cong\triangle DCB\).

Step3: Analyze corresponding parts

Since \(\triangle ABC\cong\triangle DCB\), the corresponding sides \(AC\) and \(BD\) are equal. So the diagonals of a rectangle are of the same length.

Answer:

We can prove that the diagonals of a rectangle are the same length by showing that two right - angled triangles formed by the sides and diagonals of the rectangle are congruent using the SAS congruence criterion.