Advertisements
Advertisements
प्रश्न
In the given figure, point S is any point on side QR of ΔPQR Prove that: PQ + QR + RP > 2PS
Advertisements
उत्तर
In △PQS
PQ + QS > PS ...(1) (Sum of two sides of a traingle is greater than the third side)
In △PRS
RP + RS > PS ...(2) (Sum of two sides of a traingle is greater than the third side)
Adding (1) and (2), we get
PQ + QS + RP + RS > PS + PS
∴ PQ + (QS + SR) + PR > 2PS
∴ PQ + QR + RP > 2PS ...(Q - S - R)
APPEARS IN
संबंधित प्रश्न
In ΔPQR, ∠Q = 90°, PQ = 12, QR = 5 and QS is a median. Find l(QS).
In the given figure, point G is the point of concurrence of the medians of Δ PQR. If GT = 2.5, find the lengths of PG and PT.
In the given figure, if seg PR ≅ seg PQ, show that seg PS > seg PQ.
Draw an obtuse angled Δ LMN. Draw its altitudes and denote the orthocentre by ‘O’.
Draw an isosceles triangle. Draw all of its medians and altitudes. Write your observation about their points of concurrence.
The medians of a triangle cross each other at _______
The centroid of a triangle divides each medians in the ratio _______
In any triangle the centroid and the incentre are located inside the triangle
The centroid, orthocentre, and incentre of a triangle are collinear
Identify the centroid of ∆PQR
In the given figure, A is the midpoint of YZ and G is the centroid of the triangle XYZ. If the length of GA is 3 cm, find XA
In ∆DEF, DN, EO, FM are medians and point P is the centroid. Find the following
If DE = 44, then DM = ?
In ∆DEF, DN, EO, FM are medians and point P is the centroid. Find the following
If PD = 12, then PN = ?
In ∆DEF, DN, EO, FM are medians and point P is the centroid. Find the following
If OE = 36 then EP = ?
If we join a vertex to a point on opposite side which divides that side in the ratio 1 : 1, then what is the special name of that line segment?
What is a median of a triangle?
What is the point where the medians of a triangle meet called?
