Answer:
Statement Reason
ABCD is a parallelogram Given
AD = BC Definition of parallelogram
∠DAO = ∠BCO Alternate interior angles
∠CBO = ∠ADO Alternate interior angles
ΔADO = ΔCBO ASA
BO = DO corresponding parts are congruent
AO = CO corresponding parts are congruent
Explanation:
To write the proof, we will use the following parallelogram
By the definition of parallelograms, opposite sides are congruent and parallel, do
AD = BC
Then, ∠DAO = ∠BCO because they are alternate interior angles. They are inside two parallel lines BC and AD and on opposite sides of a transversal CA.
In the same way, ∠CBO = ∠ADO because they are alternate interior angles.
Now, we can say that the triangles ADO and CBO are congruent by ASA (Angle - Side - Angle) and the corresponding part of congruent triangles are congruent so
BO = DO
AO = CO
This means that the diagonal of a parallelogram bisect one another.
Therefore, the proof is
Statement Reason
ABCD is a parallelogram Given
AD = BC Definition of parallelogram
∠DAO = ∠BCO Alternate interior angles
∠CBO = ∠ADO Alternate interior angles
ΔADO = ΔCBO ASA
BO = DO corresponding parts are congruent
AO = CO corresponding parts are congruent
