Question

which would prove that (\triangle abcsim\triangle xyz)? select two options.
(square\frac{ba}{yx}=\frac{bc}{yz}=\frac{ac}{xz})
(square\frac{ba}{yx}=\frac{bc}{yz},angle ccongangle z)
(square\frac{ac}{xz}=\frac{ba}{yx},angle acongangle x)
(square\frac{ba}{yx}=\frac{ac}{yz}=\frac{bc}{xz})
(square\frac{bc}{xy}=\frac{ba}{zx},angle ccongangle x)

Explanation:

• For \(\frac{BA}{YX}=\frac{BC}{YZ}=\frac{AC}{XZ}\):

By the Side - Side - Side (SSS) similarity criterion, if the ratios of the corresponding sides of two triangles are equal, then the two triangles are similar.

• For \(\frac{AC}{XZ}=\frac{BA}{YX},\angle A\cong\angle X\):

By the Side - Angle - Side (SAS) similarity criterion, if the ratio of two pairs of corresponding sides is equal and the included angles are congruent, then the two triangles are similar.

Answer:

\(\frac{BA}{YX}=\frac{BC}{YZ}=\frac{AC}{XZ}\), \(\frac{AC}{XZ}=\frac{BA}{YX},\angle A\cong\angle X\)