Question

Complete the Proof Statements Reasons given 3. Alternate Interior Angles Theorem AB = CD 2. כם 5. 6. 2 LD 6. Given: ABCD is a D parallelogram Prove: AE CE, DE BE ASA Triangle Congruence Theorem ABCD, AD|| CB Opposite sides of a are congruent ME - CE. DE BE ABCD is a parallelogram A E C CPCTC ZDCE ZBAE ZCDB=LIABD AABE ACDE Definition of Parallelogram​

Answer 1

Explanation:

1)
`ABCD` is a parallelogram (given)

2)
`\overline{AB} \parallel \overline{CD}, \overline{AD} \parallel \overline{CB}` (definition of parallelogram)

3)
`\angle DCE \cong \angle BAE, \angle CDB \cong \angle ABD` (Alternate interior angles theorem)

4)
`\overline{AB} \cong \overline{CD}` (opposite sides of a parallelogram are congruent)

5)
`\triangle ABE \cong \triangle CDE` (ASA Triangle Congruence theorem)

6)
`\overline{AE} \cong \overline{CE}, \overline{DE} \cong \overline{BE}` (CPCTC)