Advertisements
Advertisements
प्रश्न
In the given figure, ∠QPR = 50° and ∠PQR = 60°. Show that: SN < SR
उत्तर
In ΔRTQ,
∠RTQ + ∠TQR + ∠TRQ = 180°
90° + 60° +∠TRQ = 180°
150° + ∠TRQ = 180°
∠TRQ = 180° - 150°
∠TRQ = 30°
∠TRQ = ∠SRN = 30° ....(i)
In NSR,
∠RNS + ∠SRN = 90° ....(∵∠NSR = 90°)
∠RNS + 30° = 90° ....[from (iii)]
∠RNS = 90° - 30°
∠RNS = 60° ....(ii)
∠SRN < ∠RNS ....(from (iii) and (iv))
SN < SR.
APPEARS IN
संबंधित प्रश्न
In the given figure, ∠B < ∠A and ∠C < ∠D. Show that AD < BC.
Show that of all line segments drawn from a given point not on it, the perpendicular line segment is the shortest.
In a huge park people are concentrated at three points (see the given figure):
A: where there are different slides and swings for children,
B: near which a man-made lake is situated,
C: which is near to a large parking and exit.
Where should an ice-cream parlour be set up so that maximum number of persons can approach it?
(Hint: The parlor should be equidistant from A, B and C)
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 ΔABC, AB = 6.2cm, BC = 5.6cm and AC = 4.2cm
In ΔPQR, PR > PQ and T is a point on PR such that PT = PQ. Prove that QR > TR.
ABCD is a trapezium. Prove that:
CD + DA + AB + BC > 2AC.
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 > QS and PR > PS
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.
