Question

proving properties of a square
given: abcd is a square.
prove: (overline{ac}perpoverline{bd})
we are given that abcd is a square. if we consider triangle aeb and triangle aed, we see that side is congruent to side ad because sides of a square are congruent. we know that side ae is congruent to side ae by using the finally, we know that side de is congruent to side because the diagonals of a square bisect each other. therefore, triangle aeb is congruent to triangle aed by 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^{circ}), and diagonal

Explanation:

Step1: Identify congruent sides in the square

In a square \(ABCD\), all sides are congruent. So, side \(AB\) is congruent to side \(AD\) because sides of a square are congruent.

Step2: Use the reflexive property

We know that side \(AE\) is congruent to side \(AE\) by using the reflexive property (a segment is congruent to itself).

Step3: Identify another pair of congruent sides

We know that side \(DE\) is congruent to side \(BE\) because the diagonals of a square bisect each other.

Step4: Determine triangle congruency

Therefore, triangle \(AEB\) is congruent to triangle \(AED\) by \(SSS\) (Side - Side - Side) congruency.

Answer:

First box: \(AB\), Second box: reflexive property, Third box: \(BE\), Fourth box: \(SSS\)