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
From the following figure, prove that: AB > CD.
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.
Name the greatest and the smallest sides in the following triangles:
ΔXYZ, ∠X = 76°, ∠Y = 84°.
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 a triangle ABC, BC = AC and ∠ A = 35°. Which is the smallest side of the triangle?
ΔABC is isosceles with AB = AC. If BC is extended to D, then prove that AD > AB.
In ΔABC, BC produced to D, such that, AC = CD; ∠BAD = 125° and ∠ACD = 105°. Show that BC > CD.
In ΔPQR, PS ⊥ QR ; prove that: PQ + PR > QR and PQ + QR >2PS.
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.
