Question

congruent to side be because the diagonals of a square bisect each other. therefore, triangle aeb is congruent to triangle aed by sss congruency. we see that angle aed and angle aeb are a linear pair, and congruent by cpctc. thus, the measure of these angles will be 90, and diagonal ac is perpendicular to diagonal bd by the

Explanation:

Step1: Recall the property of perpendicular lines

If two lines intersect to form a linear pair of congruent angles, then the lines are perpendicular.

Step2: Apply the property to the given angles

Since angle \(AED\) and angle \(AEB\) are a linear pair and congruent (by \(CPCTC\) from \(\triangle AEB\cong\triangle AED\) via \(SSS\) congruency as diagonals of a square bisect each other, so \(AE = AE\), \(BE=DE\), \(AB = AD\) (sides of a square)), by the property that if a linear pair of angles is congruent, the lines forming the angles are perpendicular.

Answer:

definition of perpendicular lines.