The following is an incomplete paragraph proving that the opposite angles of parallelogram abcd are congruent: according to the given information, and . using a straightedge, extend segment ab and place point p above point b. by the same reasoning, extend segment ad and place point t to the left of point a. angles bcd and pbc are congruent by the alternate interior angles theorem. angles pbc and bad are congruent by the by the transitive property of equality, angles bcd and bad are congruent. angles abc and bat are congruent by the angles bat and cda are congruent by the corresponding angles theorem. by the transitive property of equality, ∠abc is congruent to ∠cda. consequently, opposite angles of parallelogram abcd are congruent. what theorems accurately complete the proof?

The figure above shows the lengths of thesides of a rectangle in cm. find the valuesof x and y and then the area of the rectangle.sides: top= 3x - yleft= 3y + 4bottom= 2x + yright= 2x - 3 use both methods, elimination and substitution, if possible.

The height of a flare fired from the deck of a ship in distress can be modeled by h(t)= -2(8t^2-52t-28), where h is the height of the flare above water and t is the time in seconds. a. find the time it takes the flare to hit the water.

Cone w has a radius of 8 cm and a height of 5 cm. square pyramid x has the same base area and height as cone w. paul and manuel disagree on how the volumes of cone w and square pyramid x are related. examine their arguments. which statement explains whose argument is correct and why? paul manuel the volume of square pyramid x is equal to the volume of cone w. this can be proven by finding the base area and volume of cone w, along with the volume of square pyramid x. the base area of cone w is π(r2) = π(82) = 200.96 cm2. the volume of cone w is one third(area of base)(h) = one third third(200.96)(5) = 334.93 cm3. the volume of square pyramid x is one third(area of base)(h) = one third(200.96)(5) = 334.93 cm3. the volume of square pyramid x is three times the volume of cone w. this can be proven by finding the base area and volume of cone w, along with the volume of square pyramid x. the base area of cone w is π(r2) = π(82) = 200.96 cm2. the volume of cone w is one third(area of base)(h) = one third(200.96)(5) = 334.93 cm3. the volume of square pyramid x is (area of base)(h) = (200.96)(5) = 1,004.8 cm3. paul's argument is correct; manuel used the incorrect formula to find the volume of square pyramid x. paul's argument is correct; manuel used the incorrect base area to find the volume of square pyramid x. manuel's argument is correct; paul used the incorrect formula to find the volume of square pyramid x. manuel's argument is correct; paul used the incorrect base area to find the volume of square pyramid x.