Question

The construction of triangle $\Delta A^{\prime }{C}^{\prime }B$ similar to triangle $\Delta ACB$ is shown in the figure below. Choose the correct option:

• A. $\angle CAB=\angle ACB$
• B. $\angle B{A}^{\prime }{C}^{\prime }=\angle BAC$
• C. $\frac{B{A}^{\prime }}{A^{\prime }{C}^{\prime }}=\frac{BC}{B{C}^{\prime }}$
• D. $\angle A^{\prime }B{C}^{\prime }\ne \angle CBA$

Answer 1

The correct option is B $\angle B{A}^{\prime }{C}^{\prime }=\angle BAC$

Since $\Delta ABC\sim \Delta A^{\prime }B{C}^{\prime }$
Hence $\angle B{A}^{\prime }{C}^{\prime }=\angle BAC$
($\because$ corresponding angles of similar triangles are equal.)
All other options do not satisfy the properties of similarity.