Advertisements
Advertisements
प्रश्न
In ΔABC, D is a point in the interior of the triangle. Prove that DB + DC < AB + AC.
Advertisements
उत्तर
In the ΔABC,
AB + AC > BC .....(∵ Sum of the two sides of triangle is always greater than third side.) ....(i)
Also, in the ΔBDC,
BD + DC > BC ....(ii)
Dividing (i) by (ii),
`"AB + AC"/"BD + DC" > "BC"/"BC"`
`"AB + AC"/"BD + DC" > 1`
AB + AC > BD + DC
i.e. BD + DC < AB + AC.
APPEARS IN
संबंधित प्रश्न
Show that in a right angled triangle, the hypotenuse is the longest side.
In a triangle locate a point in its interior which is equidistant from all the sides of the triangle.
How had the position of women improved in our country since independence ? Explain with examples.
In a triangle PQR; QR = PR and ∠P = 36o. Which is the largest side of the triangle?
In the following figure, write BC, AC, and CD in ascending order of their lengths.
In the following figure, ∠BAC = 60o and ∠ABC = 65o.
Prove that:
(i) CF > AF
(ii) DC > DF
"Issues of caste discrimination began to be written about in many printed tracts and essays in India in the late nineteenth century." Support the statement with two suitable examples.
Name the smallest angle in each of these triangles:
In ΔPQR, PQ = 8.3cm, QR = 5.4cm and PR = 7.2cm
In the given figure, ∠QPR = 50° and ∠PQR = 60°. Show that: SN < SR
In ΔPQR is a triangle and S is any point in its interior. Prove that SQ + SR < PQ + PR.
