Question

which of the following congruency statements is correct?

△yzx ≅ △bcd

△yzx ≅ △dcb

△zxy ≅ △dcb

△yxz ≅ △cdb

Explanation:

Step1: Match corresponding vertices

In \(\triangle YZX\) and \(\triangle DCB\):

• \(YZ = DC = 2.4\mathrm{cm}\)
• \(\angle Y = \angle D=36^{\circ}\)
• \(ZX = CB = 2.4\mathrm{cm}\)

By \(SAS\) (Side - Angle - Side) congruence criterion, we check the order of vertices.

Step2: Analyze congruence statement

For congruent triangles, the order of vertices must correspond.
In \(\triangle YZX\) and \(\triangle DCB\):

• \(Y\) corresponds to \(D\)
• \(Z\) corresponds to \(C\)
• \(X\) corresponds to \(B\)

Answer:

\(\triangle YZX\cong\triangle DCB\)