Question

Look at the parallelogram ABCD shown below: The table below shows the steps to prove that if the quadrilateral ABCD is a parallelogram, then its opposite sides are congruent:

Statement Reasons 1 AB is parallel to DC and AD is parallel to BC Definition of parallelogram 2
angle 1 = angle 2, angle 3 = angle 4 If two parallel lines are cut by a transversal then the _______________ are congruent 3
BD = BD Reflexive Property 4
triangles ADB and CBD are congruent If two angles and the included side of a triangle are congruent to the corresponding angles and side of another triangle then the triangles are congruent by ASA postulate 5
AB = DC, AD = BC Corresponding parts of congruent triangles are congruent
Which choice completes the missing information for reason 2 in the chart?
alternate interior angles
corresponding angles
same-side interior angles
vertical angles

Answer 1

alternate interior angles, i took the test and got it right

Explanation:

Answer 2

The correct option is 1.

Explanation:

Statement Reasons

1. AB is parallel to DC and Definition of parallelogram

AD is parallel to BC

2. angle 1 = angle 2, If two parallel lines are cut by a

angle 3 = angle 4 transversal then the alternate

interior angles are congruent

3. BD = BD Reflexive Property

4.
`\triangle ADB\cong \triangle CBD` ASA postulate

5. AB = DC, AD = BC (CPCTC)

If two angles and the included side of a triangle are congruent to the corresponding angles and side of another triangle then the triangles are congruent by ASA postulate.

According to alternate interior angles theorem, two parallel lines are cut by a transversal then the alternate interior angles are congruent.

Therefore option 1 is correct.