Question

Based only on the given information, it is guaranteed that ∠cBc.

Given: AABC
AB || CD
∠ACD ≅ ∠BCD
a) True
b) False

Answer 1

The given statement is true, and we can conclude that ∠cBc based on the information given.

Step-by-step explanation:

The given statement is TRUE. Based on the given information that AABC AB || CD and ∠ACD ≅ ∠BCD, we can conclude that ∠cBc.

When two parallel lines are intersected by a transversal, the corresponding angles on the same side of the transversal are congruent. Here, line AB and line CD are parallel, and line AC and line BC act as transversals. Therefore, ∠ACD and ∠BCD are corresponding angles and are congruent.

Since ∠ACD and ∠BCD are congruent and line AB and line CD are parallel, we can deduce that line AB and line BC are also parallel. Hence, we can conclude that ∠cBc.