Question

The two triangles $\Delta BCA\cong \Delta XCY$ by Side Angle Side. Show which another pair of vertical angles are congruent.

• A. $\angle ACX\ne \angle BCY$
• B. $\angle ACX\cong \angle BCY$
• C. $\angle ACX\sim \angle BCY$
• D. $\angle ACX÷\angle BCY$

Answer 1

The correct option is B $\angle ACX\cong \angle BCY$

In $\Delta BCA$ and $\Delta XCY$
$\overline{BC}=\overline{XC}$ (given C is midpoint)
$\overline{AC}=\overline{CY}$ (given C is midpoint)
$\angle BCA\cong \angle XCY$ (Vertical angles are congruent)
$\therefore \Delta BCA\cong \Delta XCY$
$\angle ACX\cong \angle BCY$ (Vertical angles are congruent)
Therefore, B is the correct answer.