Answer:
ABCD is a parallelogram
Step-by-step explanation:
Given: AD ≅ BC and AD ∥ BC Prove: ABCD is a
parallelogram. Statements Reasons 1. AD ≅ BC; AD ∥ BC
1. given 2. ∠CAD and ∠ACB are alternate interior ∠s 2.
definition of alternate interior angles 3. ∠CAD ≅ ∠ACB 3.
alternate interior angles are congruent 4. AC ≅ AC 4.
reflexive property 5. △CAD ≅ △ACB 5. SAS congruency
theorem 6. AB ≅ CD 6. ? 7. ABCD is a parallelogram 7.
if a quad. ABCD has its opposite sides congruent and adjacent side is perpendicular then the quad ABCD is the parallelogram.
Given-
The side AB is equal to the side BC.
Side AD is perpendicular to the side BC.
Now By the reflexive property of the parallelogram we can say that,
[tex]AC\cong AC[/tex]
If two perpendicular lines are cut by a transverse line then the alternate angles are equal. Thus,
[tex]\angle DAC \cong \angle ACB[/tex]
As by the above we can use the Side Angle Side rule. Therefore
[tex]\Delta ADC \cong \Delta BCA[/tex]
Now we know that the for corresponding sides of the congruent triangle,
[tex]BA\cong DC[/tex]
So, quad. ABCD is the parallelogram.
Hence, if a quad. ABCD has its opposite sides congruent and adjacent side is perpendicular then the quad ABCD is the parallelogram.
For more about the parallelogram follow the link below-
https://brainly.com/question/1563728
