CPM Homework Help : CCG Problem 7-47

If $ΔABC≅ΔDEC$ , which of the statements below must be true? Justify your conclusion. Note: More than one statement may be true.

$\overline{AC}≅\overline{DC}$

$m∠B=m∠D$

$\overline{AB}//\overline{DE}$

$AD=BE$

None of these are true.

Segment, A,D, & segment, E,B, intersect at point, c, segments from, A to b, and from D, to e, create triangles, A,B,C, & C,D,E.

Step 1:

Using the fact that the triangles are congruent, mark the angles and sides that are congruent.

Labels added to triangles: Angle A & angle D each has 1 tick mark, Angle, a,C,b, & angle, e,C,d each has 2 tick marks, Angle B & angle E each has 3 tick marks, Side, B,C, & side, C,E, each has 1 tick mark, Side, A, B, & side, D,E, each has 2 tick marks, Side, A,C, & side, C,D, each has 3 tick marks.

Step 2:

Determine which statements must be true. Do not rely on what simply looks true in the original diagram.