Question

Match the statement with the correct reason to show that ^ABC is congruent to ^DCB.

Answer 1

For this problem, we are given two triangles and we need to match the statements that give the correct reasons to show the triangles are simillar.

The first statement is:

`AC\cong BD`

This statement is given, because the image shows that the two segments are parallel. So A matches with 1.

The second statement is:

`AB\cong CD`

Which is also given. Statement B matches with 4.

The third statement is:

`\angle ABC\cong\angle DCB`

Since lines AB and CD are parallel (given), the diagonal forms a transversal line across the two parallel ones, which means that the two angles are alternate interior angles. So statement C matches with 3.

Finally we have the conclusion that both triangles are simillar, which is obtained through the SAS theorem as we have two congruent sides and one congruent angle. Statement D matches with 2.

So the correct answer is:

A -> 1

B -> 4

C -> 3

D -> 2