Question

complete this assessment to review what youve learned. it will not count toward your grade. use the image to answer the question. given that quadrilateral ( abcd ) is a rectangle, which of the following statements, once proven, will prove that the diagonals of rectangle ( abcd ) are congruent? statement #1 ( \triangle adccong\triangle cba ) statement #2 ( \triangle bcdcong\triangle dab ) statement #3 ( \triangle adccong\triangle bcd ) (1 point) statement # once proven, will prove that the diagonals of rectangle ( abcd ) are congruent

Explanation:

Step1: Recall the properties of a rectangle

In a rectangle \(ABCD\), \(AD = BC\), \(AB=CD\), and \(\angle ADC=\angle CBA = 90^{\circ}\)

Step2: Use the congruence of triangles to find the relationship between diagonals

If \(\triangle ADC\cong\triangle CBA\) (by \(SAS\) congruence: \(AD = BC\), \(\angle ADC=\angle CBA\), \(CD = AB\)), then the corresponding parts of congruent triangles are congruent. The diagonals \(AC\) and \(BD\) can be related. In \(\triangle ADC\) and \(\triangle CBA\), \(AC\) is a side of \(\triangle ADC\) and \(BD\) (since in rectangle \(ABCD\), if we consider the congruence of \(\triangle ADC\) and \(\triangle CBA\), \(AC\) (diagonal of the rectangle) and \(BD\) (diagonal of the rectangle) are corresponding sides of congruent triangles \(\triangle ADC\) and \(\triangle CBA\))

Answer:

Statement #1