Question

Fill in the boxes please

Answer 1

`Given: AD \parallel BCAD∥BC and AD=CB`

To Prove:
`AB \parallel DCAB∥DC`

1.
`AD \parallel BCAD∥BC , AD=CB`

Reason: Given

2. AC = AC

Reason: Reflexive Property of Equality

3.
`\angle 2 = \angle 3∠2=∠3`

Reason: If Lines are parallel, then Alternate Interior Angles are Equal).

4.
`\Delta ACD \cong \Delta CABΔACD≅ΔCAB`

Reason: SAS

5.
`\angle 1 = \angle 4∠1=∠4`

Reason: CPCTE

6.
`AB \parallel DCAB∥DC`

Reason: If Alternate Interior Angles are Congruent, then Lines are Parallel.

Answer 2

The missing Statements and reasons are given below

Statement >> Reason

4. CB ≅ BC >> reflexive property of congruence

5. ∠ABC ≅ ∠DCB and ∠ACB ≅ ∠DBC >> Alternate interior angles theorem

6. ΔACB ≅ ΔDBC >> ASA congruence

7. AB ≅ DC and AC ≅ DB >> CPCTC