Advertisements
Advertisements
प्रश्न
In the given figure, ∠B < ∠A and ∠C < ∠D. Show that AD < BC.

Advertisements
उत्तर
In ΔAOB,
∠B < ∠A
⇒ AO < BO (Side opposite to smaller angle is smaller) ... (1)
In ΔCOD,
∠C < ∠D
⇒ OD < OC (Side opposite to smaller angle is smaller) ... (2)
On adding equations (1) and (2), we obtain
AO + OD < BO + OC
AD < BC
संबंधित प्रश्न
In the given figure, PR > PQ and PS bisects ∠QPR. Prove that ∠PSR >∠PSQ.

Show that of all line segments drawn from a given point not on it, the perpendicular line segment is the shortest.
If two sides of a triangle are 8 cm and 13 cm, then the length of the third side is between a cm and b cm. Find the values of a and b such that a is less than b.
“Caste inequalities are still prevalent in India.” Examine the statement.
Name the greatest and the smallest sides in the following triangles:
ΔDEF, ∠D = 32°, ∠E = 56° and ∠F = 92°.
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 ΔABC, BC produced to D, such that, AC = CD; ∠BAD = 125° and ∠ACD = 105°. Show that BC > CD.
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.
