Kan somebody heplme #onsangre #on9ine3rey derek wrote the following paragraph proof for the vertical angles theorem: the sum of angle 1 and angle 4 and the sum of angle 3 and angle 4 are each equal to 180 degrees by the definition of supplementary angles. the sum of angle 1 and angle 4 is equal to the sum of angle 3 and angle 4 by the transitive property of equality. angle 1 is equal to angle 3 which phrase completes the proof? by construction using a straightedge by the definition of a perpendicular bisector by the subtraction property of equality by the vertical angles theorem

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 .