A and B are respectively the points on the sides PQ and PR of a triangle PQR such that PQ = 12.5 cm, PA = 5 cm, BR= 6 cm and PB = 4 cm. Is AB || QR? Give reasons for your answer
Solution:
Given, the points A and B lie on the sides PQ and PR of a triangle PQR.
Given, the length of the segments
PQ = 12.5 cm
PA = 5 cm
BR = 6 cm
PB = 4 cm
We have to check if AB is parallel to QR.
Basic Proportionality Theorem 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 applying Basic Proportionality theorem,
PB/BR = PA/AQ
To find AQ,
AQ = PQ - PA
AQ = 12.5 - 5
AQ = 7.5 cm
LHS: PB/BR
= 4/6
= 2/3
RHS: PA/AQ
= 5/7.5
= 50/75
= 2/3
LHS = RHS
So, the sides are divided in the same proportion.
Therefore, AB is parallel to RQ.
✦ Try This: A and B are respectively the points on the sides PQ and PR of a triangle PQR such that PQ = 10.5 cm, PA = 4 cm, BR= 5 cm and PB = 4 cm. Is AB || QR? Give reasons for your answer
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 6
NCERT Exemplar Class 10 Maths Exercise 6.2 Problem 3
A and B are respectively the points on the sides PQ and PR of a triangle PQR such that PQ = 12.5 cm, PA = 5 cm, BR= 6 cm and PB = 4 cm. Is AB || QR? Give reasons for your answer
Summary:
A and B are respectively the points on the sides PQ and PR of a triangle PQR such that PQ = 12.5 cm, PA = 5 cm, BR= 6 cm and PB = 4 cm, then AB || QR is true
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