X and Y are points on the sides AB and AC respectively of a triangle ABC such that AX/AB = 1/4. AY = 2 cm and YC = 6 cm. Find whether XY is parallel to BC or not.
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X and Y are point of the sides AB and AC respectively of a triangle ABC such that AX/AB =1/4 , AY = 2 cm and YC = 6 cm . Find wheather XY|| BC or not
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Xy is parallel to BC because a x / a b is equals to 1 divided by 4 and a y / AC is equals to 2 / 8 that is 1 / 4 so the ratio is same then xy is parallel to BC.
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saltywhitehorse
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Answer:
XY is parallel to BC
Step-by-step explanation:
Given
\frac{Ax}{AB}=\frac{1}{4}
AY=2\text{ cm}
YC=6\text{ cm}
AC=AY+YC=2+6=8\text{ cm}
The ratio between AY and AC
\frac{AY}{AC}=\frac{2}{8}\\\\\therefore\frac{AY}{YC}=\frac{1}{4}
As per the side splitter theorem if a line intersect the other two sides of a triangle and the line divides those two sides proportionally then the line is parallel to the third side of a triangle.
Therefore,
XY\parallel BC
Step-by-step explanation:
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