Original scale: 1 inch = 4 feet. A square with 12-foot sides and a larger square with 15-foot sides. Raphael saw a square patio that was 12-feet long on each side. He wants to build a patio that will be 15-feet long on each side. The change in the scale factor is. The change of scale means that 1 inch represented 4 feet, but now 1 inch represents feet.

Given: abcd is a square. prove: ac ? 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°, and diagonal ac is perpendicular to diagonal bd by the .