If P and Q are the midpoints of sides YZ and XZ respectively i

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Solution

Q.
A farmer had a triangular piece of land. He put a fence, parallel to one of the sides of the field as shown in the figure.

Based on the above information answer the following questions:

(iii) (b) If P and Q are the midpoints of sides YZ and XZ respectively in $Δ Z Y X$ , then state whether $P Q ∥ Y X$ or not. Give reason.

1 $P Q ∥ Y X$

2 $P X ∥ Y Q$

3 $Q X ∥ Y P$

4 $- P X ∥ Y Q$

Ans.
(1)

$I n Δ Z Y X,$ P and Q are midpoints of side YZ and XZ respectively.

$\frac{Z P}{P Y} = 1 and \frac{Z Q}{Q X} = 1 \Rightarrow \frac{Z P}{P Y} = \frac{Z Q}{Q X} \Rightarrow P Q ∥ Y X (By converse of BPT) Y e s, P Q ∥ Y X .$

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