Question

B-007_1113Given: ABCD is a parallelogram.Prove: AB CD and BC DABADCorrect! Assemble the nextstatementAngles Segments Triangles Statements ReasonsASACPCTCgivenalternate interior angles theoremStatementsI. ADCO IS a paranciogram✓2. AB || CD3. BC || DA4. draw AC5. ZBCA and ZDACare alt. interior angles✓6. ZDCA and ZBACare alt. interior anglesAC✓7. ACReasons1 given2. def. of parallelogram3. def. of parallelogram4. unique line postulate5. def. of alt. interior angles6. def. of alt interior angles7. reflexive property8

Answer 1

Given:

ABCD is a parallelogram.

Required:

We need to prove

$\text{ AB}\cong\text{CD and BC}\cong\text{DA}$

Explanation:

We know that alternate interior angles are congruent.

$\angle BCA\cong\angle DAC$$\angle DCA\cong\angle BAC$$AC\cong AC$

The ASA Postulate. If two angles and the included side of one triangle are congruent to two angles and the included side of a second triangle, then the triangles are congruent.

$\Delta ABC\cong\Delta ACD$

Reason ASA postulates.

Final answer:

Statements

8)

$\Delta ABC\cong\Delta ACD$

Reason

8)

ASA postulates