Triangles \(ACD\) and \(BCD\) are isosceles. Angle \(BAC\) has a measure of 18 degrees, and angle \(BDC\) has a measure of 48 degrees. Find the measure of angle \(ABD\).

Here are some statements about two zigzags. Put them in order to prove figure \(ABC\) is congruent to figure \(DEF\).

Two figures, A B C and D E F, each composed of two line segments that share an endpoint . A B slants upward and to the left and B C slants upward and to the right. Figure D E F is below and to the right of figure A B C. D E slants upward and to the left and E F slants upward and slightly to the left. B C and E F have one tick mark. A B and D E have two tick marks. Angles B and E marked equal.

• 1: If necessary, reflect the image of figure \(ABC\) across \(DE\) to be sure the image of \(C\), which we will call \(C'\), is on the same side of \(DE\) as \(F\). 
• 2: \(C'\) must be on ray \(EF\) since both \(C'\) and \(F\) are on the same side of \(DE\) and make the same angle with it at \(E\).
• 3: Segments \(AB\) and \(DE\) are the same length, so they are congruent. Therefore, there is a rigid motion that takes \(AB\) to \(DE\). Apply that rigid motion to figure \(ABC\).
• 4: Since points \(C'\) and \(F\) are the same distance along the same ray from \(E\), they have to be in the same place.
• 5: Therefore, figure \(ABC\) is congruent to figure \(DEF\).

Match each statement using only the information shown in the pairs of congruent triangles.