Question

Given AD || BC and ∠BCD ≅ ∠ADC, prove DE || CE.

a) ZADC, ZBCD, ZCBE, ZCEB, 2DAE, ZDEA, ZECD, LEDC
b) A, B, C, E, D
c) Statements: ZADC, ZBCD, ZCBE, ZCEB, 2DAE, ZDEA, ZECD, LEDC; Reasons: A, B, C, E, D
d) Statements: A, B, C, E, D; Reasons: ZADC, ZBCD, ZCBE, ZCEB, 2DAE, ZDEA, ZECD, LEDC

Answer 1

To prove that DE || CE, we can use the given information and the properties of parallel lines and corresponding angles.

Step-by-step explanation:

To prove that DE || CE, we can use the given information and the properties of parallel lines and corresponding angles.

1. By the given information AD || BC and ∠BCD ≅ ∠ADC.
2. Using the property that corresponding angles are congruent, we have ∠BCD ≅ ∠ADC.
3. Since AD || BC, the alternate interior angles ∠ADC and ∠CDE are congruent.
4. Therefore, by the Transitive Property of Congruence, ∠CDE ≅ ∠BCD.
5. Finally, using the Converse of the Corresponding Angles Postulate, we can conclude that DE || CE.