P and Q are the points on the sides DE and DF of a triangle DEF such that DP = 5 cm, DE = 15 cm, DQ= 6 cm and QF = 18 cm. Is PQ||EF? Give reasons for your answer
Solution:
Given, the points P and Q lie on the sides DE and DF of a triangle DEF.
Also, DP = 5 cm
DE = 15 cm
DQ = 6 cm
QF = 18 cm
We have to check if PQ is parallel to EF.
Basic Proportionality Theorem(BPT) states that if a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided in the same ratio.
By BPT,
DP/PE = DQ/QF
PE = DE - DP = 15 - 5 = 10 cm
LHS: DP/PE
= 5/10
= 1/2
RHS: DQ/QF
= 6/18
= 1/3
LHS ≠ RHS
BPT is not satisfied.
Therefore, PQ is not parallel to EF.
✦ Try This: P and Q are the points on the sides DE and DF of a triangle DEF such that DP = 6 cm, DE = 11 cm, DQ= 8 cm and QF = 9 cm. Is PQ||EF? Give reasons for your answer
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 6
NCERT Exemplar Class 10 Maths Exercise 6.2 Sample Problem 2
P and Q are the points on the sides DE and DF of a triangle DEF such that DP = 5 cm, DE = 15 cm, DQ= 6 cm and QF = 18 cm. Is PQ||EF? Give reasons for your answer
Summary:
P and Q are the points on the sides DE and DF of a triangle DEF such that DP = 5 cm, DE = 15 cm, DQ= 6 cm and QF = 18 cm. PQ is not parallel to EF as it fails to satisfy the conditions of basic proportionality theorem
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