Match each statement in the proof with the correct reason.
options: definition of parallelogram
definition of diagonal
given
same-side interior angles theorem
alternate interior angles theorem
definition of supplementary
definition of same-side interior angles

See explanation

Step-by-step explanation:

Definition of parallelogram: Parallelogram is a quadrilateral with two pairs of parallel sides.    

Definition of transversal (diagonal): A line that cuts across two or more (usually parallel) lines.

Definition of the same side interior angles: These angles are located exactly as their name describes. They are "interior" (between the parallel lines), and they are on the same side of the transversal (diagonal).

The same-side interior angles theorem states that when two lines that are parallel are intersected by a transversal line, the same-side interior angles that are formed are supplementary

       Statement                          Reason

1. ABCD is a parallelogram  -  Given

2.                           -  Definition of parallelogram

3. is a diagonal of and - Definition of diagonal

4.   and are the same side interior angles - Definition of same-side interior angles

5.   is supplementary to   - Same-Side Interior Angles Theorem

d) by the cross product property, ab^2 = bc multiplied by ad

step-by-step explanation:

we are given

in the given triangle abc

angle a is 90° and segment ad is perpendicular to segment bc

we can see that

triangle(abc) and triangle(abd) are similar because they have common side and same angle (90 degree)

so, triangles(abc) and abd are similar

since, they are similar

so, the ratio of their sides must be equal

we get

now, we can cross multiply

and we get

so, this could be step to prove it