Advertisements
Advertisements
प्रश्न
In ΔPQR, PR > PQ and T is a point on PR such that PT = PQ. Prove that QR > TR.
Advertisements
उत्तर
In ΔPQT, we have
PT = PQ ...(1)
In ΔPQR,
PQ + QR > PR
PQ + QR > PT + TR
PQ + QR > PQ + TR ...[Using (1)]
QR > TR
Hence, proved.
APPEARS IN
संबंधित प्रश्न
AB and CD are respectively the smallest and longest sides of a quadrilateral ABCD (see the given figure). Show that ∠A > ∠C and ∠B > ∠D.
Show that of all line segments drawn from a given point not on it, the perpendicular line segment is the shortest.
D is a point in side BC of triangle ABC. If AD > AC, show that AB > AC.
“Caste inequalities are still prevalent in India.” Examine the statement.
Arrange the sides of the following triangles in an ascending order:
ΔABC, ∠A = 45°, ∠B = 65°.
Name the smallest angle in each of these triangles:
In ΔPQR, PQ = 8.3cm, QR = 5.4cm and PR = 7.2cm
Name the smallest angle in each of these triangles:
In ΔXYZ, XY = 6.2cm, XY = 6.8cm and YZ = 5cm
In the given figure, ∠QPR = 50° and ∠PQR = 60°. Show that : PN < RN
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.
In ΔABC, D is a point in the interior of the triangle. Prove that DB + DC < AB + AC.
