Advertisements
Advertisements
प्रश्न
In ΔPQR is a triangle and S is any point in its interior. Prove that SQ + SR < PQ + PR.
Advertisements
उत्तर
In ΔPQR,
PQ + PR > QR ....(∵ Sum of two sides of a triangle is always greater than the third side.) ....(i)
Also, in ΔSQR,
SQ + SR > QR ....(∵ Sum of two sides of a triangle is always greater than the third side.) ....(ii)
Dividing (i) by (ii),
`"PQ + PR"/"SQ + SR" > "QR"/"QR"`
`"PQ + PR"/"SQ + SR" > 1`
PQ + PR > SQ + SR
i.e. SQ + SR < PQ + PR.
APPEARS IN
संबंधित प्रश्न
Show that of all line segments drawn from a given point not on it, the perpendicular line segment is the shortest.
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?
In the following figure, write BC, AC, and CD in ascending order of their lengths.
“Caste inequalities are still prevalent in India.” Examine the statement.
Name the greatest and the smallest sides in the following triangles:
ΔXYZ, ∠X = 76°, ∠Y = 84°.
ΔABC is isosceles with AB = AC. If BC is extended to D, then prove that AD > AB.
Prove that the perimeter of a triangle is greater than the sum of its three medians.
D is a point on the side of the BC of ΔABC. Prove that the perimeter of ΔABC is greater than twice of AD.
In the given figure, T is a point on the side PR of an equilateral triangle PQR. Show that RT < QT
ΔABC in a isosceles triangle with AB = AC. D is a point on BC produced. ED intersects AB at E and AC at F. Prove that AF > AE.
