The missing statements that completes the proof that proves that quadrilateral ACDB is a parallelogram is explained below.
What are the Properties of a Parallelogram?
A quadrilateral that has the following properties is a parallelogram, in reference to the quadrilateral ACDB in the image given:
- Opposite sides are congruent (AB ≅ CD and AC ≅ BD).
- Opposite angels are congruent to each other (∠A ≅ ∠D and ∠C ≅ ∠B).
- Consecutive angles are supplementary (m∠A + m∠C = 180°).
Given that ΔCFD ≅ ΔBGA, the proof that quadrilateral ACDB is a parallelogram is given below:
Since we know that ΔCFD ≅ ΔBGA, therefore, CD ≅ BA because corresponding parts of congruent triangles are: congruent.
Since we also know that m∠DCA + m∠CAB = 180°, then we also know that both angles are: supplementary.
Transversal A.F cut the two lines, CD and BA, then the interior angles on the same side of the transversal are: supplementary, thus, we it implies we know that lines CD and BA would be: parallel.
Since one pair of sides (CD and BA) are both parallel and congruent, then we know that quadrilateral ACDB is a parallelogram.
Learn more about parallelogram on:
https://brainly.com/question/20526916
#SPJ1
