Advertisements
Advertisements
Question
In the given figure, point S is any point on side QR of ΔPQR Prove that: PQ + QR + RP > 2PS
Advertisements
Solution
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
RELATED QUESTIONS
The length of hypotenuse of a right angled triangle is 15. Find the length of median of its hypotenuse.
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 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 ∆ABC, AD is the bisector of ∠A meeting BC at D, CF ⊥ AB and E is the mid-point of AC. Then median of the triangle is ______.
What is a median of a triangle?
The centroid divides each median in what ratio?
In a triangle, where is the centroid always located?
