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. it is congruent to itself by the reflexive property of equality. angles bca and dac are congruent by the same reasoning. 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?

a) angles abc and cda are corresponding parts of congruent triangles, which are congruent (cpctc).

b) angles abc and cda are congruent according to a property of parallelograms (opposite angles congruent).

c) angles bac and dca are congruent by the same-side interior angles theorem.

d) angles bac and dca are congruent by the alternate interior angles theorem.

D. Angles BAC and DCA are congruent by the Alternate interior angles theorem.

Step-by-step explanation:

Given ABCD is a parallelogram.

AB=CD and BC=AD

To prove that .

Proof: According to given information

and segment .

Construct diagonal AC with a straightedge.

In

AC=AC

Reflexive property of equality.

By alternate interior angles theorem.

By alternate interior angles theorem.

By ASA( Angle-Side_Angle) theorem.

By CPCTC opposite sides AB and CD, as well as BC and DA are congruent.

Hence proved.

sine

step-by-step explanation:

starting with:    

5 + x - 12 = 2x - 7   

5 + x - 12 - x = 2x - 7 - x (subtract x from both sides)   

5 - 12 = x - 7 (combine and cancel x's from both sides)   

5 - 12 + 7 = x - 7 + 7 (add 7 to both sides)   

0 = x (add numbers together on both sides)       

so in order for the equation to be true, x must be 0.   

trying x = -0.5   

5 + x - 12 = 2x - 7 (original equation)   

5 + -0.5 - 12 = 2(-0.5) - 7 (plug in value of x)   

5 + -0.5 - 12 = -1 - 7 (did multiplication)   

-7.5 = -8 (did addition on both sides)       

since -7.5 is obviously not equal to -8, the value of -0.5 for x is wrong.   

trying x = 0   

5 + x - 12 = 2x - 7 (original equation)   

5 + 0 - 12 = 2(0) - 7 (plug in value of x)   

5 + 0 - 12 = 0 - 7 (did multiplication)   

-7 = -7 (did addition on both sides)       

since -7 equals -7, that demonstrates that the value of 0 for x is correct.   

trying x = 1   

5 + x - 12 = 2x - 7 (original equation)   

5 + 1 - 12 = 2(1) - 7 (plug in value of x)   

5 + 1 - 12 = 2 - 7 (did multiplication)   

-6 = -5 (did addition on both sides)       

since -6 is obviously not equal to -5, the value of 1 for x is wrong.