Through A, B and C, lines RQ, PR and QP have been drawn, respectively parallel to sides BC, CA and AB of a ∆ ABC as shown in Fig.8.5. Show that BC = 1/2 QR.
Solution:
Given, ABC is a triangle
Lines RQ, PR and QP are drawn through A, B and C parallel to sides BC, CA and AB of the triangle ABC.
We have to show that BC = 1/2 QR
Given, RQ || BC
PR || AC
QP || AB
Considering quadrilateral BCAR,
BR || CA
RA || BC
We know the opposite sides of a parallelogram are parallel and congruent.
So, BCAR is a parallelogram.
BC = AR ------------------ (1)
Considering quadrilateral BCQA,
BC || AQ
AB || QC
So, BCQA is a parallelogram
BC = AQ ------------------ (2)
Adding (1) and (2),
BC + BC = AR + AQ
2BC = AR + AQ
From the figure,
AR + AQ = RQ
So, 2BC = RQ
Therefore, BC = 1/2 QR
✦ Try This: In parallelogram ABCD, two point P and Q are taken on diagonal BD such that DP = BQ. Show that △AQB ≅ △CPD
☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 8
NCERT Exemplar Class 9 Maths Exercise 8.3 Problem 7
Through A, B and C, lines RQ, PR and QP have been drawn, respectively parallel to sides BC, CA and AB of a ∆ ABC as shown in Fig.8.5. Show that BC = 1/2 QR.
Summary:
Through A, B and C, lines RQ, PR and QP have been drawn, respectively parallel to sides BC, CA and AB of a ∆ ABC as shown in Fig.8.5. It is shown that BC = 1/2 QR
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