4 lines extend from point B. A line extends straight up from B to point A. Another line extends up and to the right to point C. Another line extends slight up and to the right to point D. The other line extends slightly down and to the right to point E.
Given that ∠ABC ≅ ∠DBE, which statement must be true?
∠ABC ≅ ∠ABD
∠ABD ≅ ∠CBE
∠CBD ≅ ∠DBE
∠CBD ≅ ∠ABC
The correct statement must be:
∠CBD ≅ ∠DBE
∠ABC ≅ ∠DBE is given in the problem. To determine which statement must be true, we need to consider the angles formed by these lines.
Since ∠ABC ≅ ∠DBE,
∠ABC and ∠DBE are congruent.
Now let's examine the options:
1. ∠ABC ≅ ∠ABD: We don't have any information about ∠ABD in the problem, so we cannot conclude its congruence with ∠ABC.
2. ∠ABD ≅ ∠CBE: We also don't have any information about ∠ABD and ∠CBE, so we cannot conclude their congruence.
3. ∠CBD ≅ ∠DBE: This statement is not supported by the given information. We only know that ∠ABC ≅ ∠DBE, not ∠CBD.
4. ∠CBD ≅ ∠ABC: This is the correct statement. Since ∠ABC ≅ ∠DBE, we can conclude that ∠CBD ≅ ∠ABC.
Therefore, the correct statement is ∠CBD ≅ ∠ABC.