Advertisements
Advertisements
Question
In ΔPQR, PS ⊥ QR ; prove that: PQ > QS and PR > PS
Advertisements
Solution
In ΔPQS,
PS ⊥ QR ....(Given)
PS < PR ....(Of all the straight lines that can be drawn to a given straight line from a point outside it, the perpendicular is the shortest.)
I.e. PR > PS.
APPEARS IN
RELATED QUESTIONS
AB and CD are respectively the smallest and longest sides of a quadrilateral ABCD (see the given figure). Show that ∠A > ∠C and ∠B > ∠D.
In the given figure, PR > PQ and PS bisects ∠QPR. Prove that ∠PSR >∠PSQ.
Arrange the sides of ∆BOC in descending order of their lengths. BO and CO are bisectors of angles ABC and ACB respectively.
Name the greatest and the smallest sides in the following triangles:
ΔDEF, ∠D = 32°, ∠E = 56° and ∠F = 92°.
Arrange the sides of the following triangles in an ascending order:
ΔABC, ∠A = 45°, ∠B = 65°.
Arrange the sides of the following triangles in an ascending order:
ΔDEF, ∠D = 38°, ∠E = 58°.
Name the smallest angle in each of these triangles:
In ΔABC, AB = 6.2cm, BC = 5.6cm and AC = 4.2cm
In ΔABC, the exterior ∠PBC > exterior ∠QCB. Prove that AB > AC.
For any quadrilateral, prove that its perimeter is greater than the sum of its diagonals.
In ΔABC, AE is the bisector of ∠BAC. D is a point on AC such that AB = AD. Prove that BE = DE and ∠ABD > ∠C.
