2. Diagonals of a parallelogram bisect each other.
3. Vertical angles are equal.
4. Definition of parallelogram.
5. If lines parallel, then alternate interior angles are equal.
The first statement is a parallelogram ABCD, which is already given in the question. So, reason 1 is: Given.
BT and TD are equal because for a parallelogram, its diagonal bisect each other. Here, BD and AC are the diagonals of parallelogram ABCD. So, the diagonals bisect each other at T. Hence,
Angles 1 and 2 is a pair of vertical angles. A pair of vertical angles are always equal to each other.
A parallelogram is a quadrilateral whose opposite sides are parallel and equal. Hence, is because of the definition of a parallelogram.
Angles 3 and 4 is a pair of alternate interior angles. If two lines are parallel, then the alternate interior angles are always equal.
The triangles BET and DFT are now congruent because:
ii. Side -
iii. Angle -
Therefore, by ASA postulate the two triangles are congruent.
As the two triangles are congruent, then their corresponding parts are also equal.
So, by CPCTE,
my answer was deleted because it was to vague the answer is 12.76 becuase its in the hundreths place. john