Advertisements
Advertisements
प्रश्न
D is a point in side BC of triangle ABC. If AD > AC, show that AB > AC.
Advertisements
उत्तर
In ΔADC
AD > AC
⇒ ∠ACD > ∠ADC ...(i)
In ΔABD
∠ABD + ∠BAD = ∠ADC ...(ii)
Putting the value of ∠ADC in equation (i)
∠ACD > ∠ABD + ∠BAD ...(iii)
⇒ ∠ACD > ∠ABD
⇒ ∠ACB > ∠ABC
AB > AC
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.
In a triangle locate a point in its interior which is equidistant from all the sides of the triangle.
From the following figure, prove that: AB > CD.
In a triangle PQR; QR = PR and ∠P = 36o. Which is the largest side of the triangle?
"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.
In ΔABC, the exterior ∠PBC > exterior ∠QCB. Prove that AB > AC.
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 trapezium. Prove that:
CD + DA + AB + BC > 2AC.
In ΔPQR is a triangle and S is any point in its interior. Prove that SQ + SR < PQ + PR.
