MCQ 511 Mark
In $\triangle\text{ABC},$ a line $XY$ parallel to $BC$ cuts $AB$ at $X$ and $AC$ at $Y$. If $BY$ bisects $\angle\text{XYC},$ then:
- ✓$\text{BC} = \text{CY}$
- B$\text{BC} = \text{BY}$
- C$\text{BC}\neq\text{ CY}$
- D$\text{BC}\neq\text{ BY}$
Answer
View full question & answer→Correct option: A.
$\text{BC} = \text{CY}$
Given: $XY || BC$ and $BY$ is bisector of $\angle\text{XYC}.$
Since $XY || BC$
So, $\angle\text{YBC}=\angle\text{BYC}$ (Alternate angles)
Now, in triangle BYC two angles are equal. Therefore, the two corresponding sides will be equal.
Hence, $BC = CY$
Hence option $(a)$ is correct.
Since $XY || BC$
So, $\angle\text{YBC}=\angle\text{BYC}$ (Alternate angles)
Now, in triangle BYC two angles are equal. Therefore, the two corresponding sides will be equal.
Hence, $BC = CY$
Hence option $(a)$ is correct.