P and Q are points on sides AB and AC respectively of Δ ABC. For each of the following cases, state whether PQ || BC.

(i) AP= 8 cm, PB = 3 cm, AC = 22 cm and AQ =16 cm.

(ii) AB= 1.28 cm, AC = 2.56 cm, AP= 0.16 cm and AQ = 0.32 cm

(iii) AB = 5 cm, AC =10 cm, AP= 4 cm, AQ = 8 cm.

(iv) AP= 4 cm, PB= 4.5 cm, AQ = 4 cm, QC = 5 cm.

(i) Given: AP= 8 cm, PB = 3 cm, AC = 22 cm and AQ =16 cm

To find: PQ || BC

In ABC,

Basic Proportionality theorem which states that if a line is drawn parallel to one side of a triangle the other two sides in distinct points, then the other two sides are divided in the same ratio.

Hence, PQ || BC [by converse of basic proportionality theorem]

Hence, Proved.

(ii) Given: AB= 1.28 cm, AC = 2.56 cm, AP= 0.16 cm and AQ = 0.32 cm

To find: PQ || BC

In ABC,

Basic Proportionality theorem which states that if a line is drawn parallel to one side of a triangle the other two sides in distinct points, then the other two sides are divided in the same ratio.

Hence, PQ || BC [by converse of basic proportionality theorem]

Hence, Proved.

(iii) Given: AB = 5 cm, AC =10 cm, AP= 4 cm, AQ = 8 cm

To find: PQ || BC

In ABC,

Basic Proportionality theorem which states that if a line is drawn parallel to one side of a triangle the other two sides in distinct points, then the other two sides are divided in the same ratio.

Hence, PQ || BC [by converse of basic proportionality theorem]

Hence, Proved.

(iv) Given: AP= 4 cm, PB= 4.5 cm, AQ = 4 cm, QC = 5 cm

To find: PQ || BC

In ABC,

Basic Proportionality theorem which states that if a line is drawn parallel to one side of a triangle the other two sides in distinct points, then the other two sides are divided in the same ratio.

⇒ PQ is not parallel to BC