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

Answer:

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