The following is an incomplete paragraph proving that the opposite sides of parallelogram abcd are congruent: parallelogram abcd is shown where segment ab is parallel to segment dc and segment bc is parallel to segment ad. according to the given information, segment ab is parallel to segment dc and segment bc is parallel to segment ad.. construct diagonal a c with a straightedge. angles bac and dca are congruent by the alternate interior angles theorem. angles bca and dac are congruent by the same theorem. triangles bca and dac are congruent according to the angle-side-angle (asa) theorem. by cpctc, opposite sides ab and cd, as well as sides bc and da, are congruent. which sentence accurately completes the proof? angles bac and dca are congruent by the same-side interior angles theorem. diagonal bd is congruent to itself by the reflexive property of equality diagonal ac is congruent to itself by the reflexive property of equality. angles abc and cda are congruent according to a property of parallelograms (opposite angles congruent).

The answer is ,Diagonal AC is congruent to itself by the Reflexive Property of Equality.Because the problem is solved by proving the congruency of two triangles ΔABC and ΔADC. Two angles of these triangles are congruent. ∠BAC cogruent ∠DCA  and ∠BCA congruent ∠DCA. for provining congruency of triangles by the theorem ASA we need two angle and one side in between these angles.Here angles are given we need the side between these angles, which is diagonal AC.

-3

step-by-step explanation:

a drawing really does here:

so i draw the horizontal line y=2 and the vertical line x=-2 at this intersection i put b (this is where my right angle is going to be).   so point b is at (-2,2).   point a is 5 units long and is also on y=2 so this point has to be (3,2) or (-7,2) -doesn't matter i will go with (3,2).

now we know c is at (-2,y) we don't know the y yet bet we know that c is on x=-2.

we have the area of the triangle is .5bh=12.5

we know the base length is 5 (ab)

we have the height is (2-y) if you look at your

plug in

.5(5)(2-y)=12.5

solve for y to get the y-coordinate for c

2.5(2-y)=12.5

divide both sides by 2.5 giving:

2-y=5

now subtract 2 on both sides

-y=3

y=-3