Question

In $\Delta HKI,\overline{HJ}$ is a perpendicular bisector of $\overline{KI}$. By which criterion will you prove $\Delta HJK\sim \Delta HJI$.

• A. SAS similarity criterion
• B. AAA similarity criterion
• C. AA similarity criterion
• D. SSS similarity criterion

Answer 1

Answer: (A)

SAS similarity criterion

In $\Delta HJK$ and $\Delta HJI$
$\overline{HJ}=\overline{HJ}$ (given $\overline{HJ}$ is a perpendicular bisector of $\overline{KI}$)
$\angle HJK$ and $\angle HJI$ (definition of perpendicular lines)
$\angle HJK=\angle HJI$ (right angles)

$\overline{KJ}=\overline{JI}$ (J is midpoint)
$\Delta HJK\sim \Delta HJI$ (SAS similarity criterion)
Therefore, A is the correct answer.