Advertisements
Advertisements
प्रश्न
In the given figure, ∠QPR = 50° and ∠PQR = 60°. Show that : PN < RN
Advertisements
उत्तर
In the given ΔPQR,
PS < PR .....(Of all the straight lines that can be drawn to a given straight line from a point outside it, the perpendicular is the shortest)
PN < PR ....(i) (∵ PN < PS)
Also,
RT < PR .....(Of all the straight lines that can be drawn to a given straight line from a point outside it, the perpendicular is the shortest)
RN < PR .....(ii) (∵ RN < RT)
Dividing (i) bt (ii),
`"PN"/"RN" < "PR"/"PR"`
`"PN"/"RN" < 1`
PN < RN.
APPEARS IN
संबंधित प्रश्न
Complete the hexagonal and star shaped rangolies (see the given figures) by filling them with as many equilateral triangles of side 1 cm as you can. Count the number of triangles in each case. Which has more triangles?
Arrange the sides of ∆BOC in descending order of their lengths. BO and CO are bisectors of angles ABC and ACB respectively.
Name the smallest angle in each of these triangles:
In ΔXYZ, XY = 6.2cm, XY = 6.8cm and YZ = 5cm
D is a point on the side of the BC of ΔABC. Prove that the perimeter of ΔABC is greater than twice of AD.
ABCD is a quadrilateral in which the diagonals AC and BD intersect at O. Prove that AB + BC + CD + AD < 2(AC + BC).
ABCD is a trapezium. Prove that:
CD + DA + AB + BC > 2AC.
ABCD is a trapezium. Prove that:
CD + DA + AB > BC.
In the given figure, ∠QPR = 50° and ∠PQR = 60°. Show that: SN < SR
In ΔPQR, PS ⊥ QR ; prove that: PQ > QS and PR > PS
Prove that in an isosceles triangle any of its equal sides is greater than the straight line joining the vertex to any point on the base of the triangle.
