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14. Quadrilaterals
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Q5 of 95 Page 15

In a ΔABC, E and F are the mid-points of AC and AB respectively. The altitude AP to BC intersects EF at Q. Prove that AQ=QP.

Given,


In ΔABC,


E & F are the mid-points of AC and AB



EF ⎸⎸BC


SO, FQ ⎸⎸BP


Q is the mid point of AP


AQ = QP (Proved)


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3

In a triangle, P, Q and R are the mid-points of sides BC, CA and AB respectively. If AC = 21 cm, BC = 29 cm and AB= 30 cm, find the perimeter of the quadrilateral ARPQ.

4

In a ΔABC, median AD is produced to X such that AD=DX. Prove that ABXC is a parallelogram.

6

In a ΔABC, BM and CN are perpendiculars from B and C respectively on any line passing through A. If L is the mid-point of BC, prove that ML=NL.

7

In Fig. 14.95, triangle ABC is right-angled at B. Given that AB=9 cm, AC=15 cm and D, E are the mid-points of the sides AB and AC respectively, calculate


(i) The length of BC


(ii) The area of ΔADE.

Questions · 95
14. Quadrilaterals
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