Advertisements
Advertisements
प्रश्न
In the given figure, seg PS is the median of ∆PQR and PT ⊥ QR. Prove that,
PR2 = PS2 + QR × ST + `("QR"/2)^2`
उत्तर
Seg PS is the median of ∆PQR ...(Given)
∴ QS = SR = `1/2`QR ...(1) [S is the midpoint of side QR]
In ∆PTS, ∠PTS = 90° ...(Given)
∴ by Pythagoras theorem,
PS2 = PT2 + TS2 ...(2)
In ∆PTR, ∠PTR = 90° ...(Given)
∴ by Pythagoras theorem,
PR2 = PT2 + TR2
∴ PR2 = PT2 + (TS + SR)2 ...(T-S-R)
∴ PR2 = PT2 + TS2 + 2ST2.SR + SR2 ...[(a + b)2 = a2 + 2ab + b2]
∴ PR2 = (PT2 + TS2) + 2ST.SR + SR2
∴ PR2 = PS2 + 2ST.`(("QR")/2) + (("QR")/2)^2` ...[From (1) and (2)]
∴ PR2 = PS2 + QR × ST + `(("QR")/2)^2`
APPEARS IN
संबंधित प्रश्न
In ∆ABC, point M is the midpoint of side BC. If, AB2 + AC2 = 290 cm2, AM = 8 cm, find BC.
Out of the following, which is the Pythagorean triplet?
Some question and their alternative answer are given.
In a right-angled triangle, if sum of the squares of the sides making right angle is 169 then what is the length of the hypotenuse?
Some question and their alternative answer are given. Select the correct alternative.
Altitude on the hypotenuse of a right angled triangle divides it in two parts of lengths 4 cm and 9 cm. Find the length of the altitude.
Some question and their alternative answer are given. Select the correct alternative.
In ∆ABC, AB = \[6\sqrt{3}\] cm, AC = 12 cm, BC = 6 cm. Find measure of ∠A.
Find the height of an equilateral triangle having side 2a.
Do sides 7 cm, 24 cm, 25 cm form a right angled triangle ? Give reason
Find the length a diagonal of a rectangle having sides 11 cm and 60 cm.
In ∆RST, ∠S = 90°, ∠T = 30°, RT = 12 cm then find RS and ST.
Prove that the sum of the squares of the diagonals of a parallelogram is equal to the sum of the squares of its sides.
Seg PM is a median of ∆PQR. If PQ = 40, PR = 42 and PM = 29, find QR.
Seg AM is a median of ∆ABC. If AB = 22, AC = 34, BC = 24, find AM
If hypotenuse of a right angled triangle is 5 cm, find the radius of
the circle passing through all vertices of the triangle.
Choose the correct alternative:
Out of given triplets, which is not a Pythagoras triplet?
Choose the correct alternative:
Out of given triplets, which is not a Pythagoras triplet?
"The diagonals bisect each other at right angles." In which of the following quadrilaterals is the given property observed?
