Question

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

Answer 1

∠ABD ≅ ∠CBE

Reason: m∠ABD = m∠ABC + m∠CBD, and m∠CBE = m∠CBD + m∠DBE. Since m∠ABC = m∠DBE, the two sums are equal, so ∠ABD ≅ ∠CBE.