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
1. ab is parallel to dc and ad is parallel to bc
2. angle 1 = angle 2, angle 3 = angle 4
3. bd = bd
4. triangles adb and cbd are congruent
5. ab = dc,
ad = bc

reasons
1. definition of parallelogram
2. if two parallel lines are cut by a transversal then the alternate interior angles are congruent
3.
4. 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
5. corresponding parts of congruent triangles are congruent

which choice completes the missing information for reason 3 in the chart?

associative property
reflexive property
substitution property
transitive property

Reflexive Property

Explanation:

In step #3, we are given that BD is equal to itself.  

The property that tells us that something is equal to itself is the reflexive property; that is our answer.

(B) Reflexive property

Step-by-step explanation:

To prove:  If the quadrilateral ABCD is a parallelogram, then its opposite sides are congruent.

Proof:

Statement                                                             Reason

1. AB is parallel to DC                       Definition of parallelogram

and AD is parallel to BC  

2.∠1=∠2                            

and ∠3=∠4              If two parallel lines are cut by a transversal then the alternate interior angles are congruent

3. BD=BD                     Reflexive  property

4. ΔADB≅ΔCBD     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

5. AB = DC,  

AD = BC          Corresponding parts of congruent triangles are congruent

Hence proved

Thus, option B is correct.

m a t h w a y. c o m

step-by-step explanation: