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
In a triangle locate a point in its interior which is equidistant from all the sides of the triangle.
In the following figure, write BC, AC, and CD in ascending order of their lengths.
"Issues of caste discrimination began to be written about in many printed tracts and essays in India in the late nineteenth century." Support the statement with two suitable examples.
Name the greatest and the smallest sides in the following triangles:
ΔXYZ, ∠X = 76°, ∠Y = 84°.
ΔABC is isosceles with AB = AC. If BC is extended to D, then prove that AD > AB.
Prove that the perimeter of a triangle is greater than the sum of its three medians.
In ΔABC, BC produced to D, such that, AC = CD; ∠BAD = 125° and ∠ACD = 105°. Show that BC > CD.
In the given figure, T is a point on the side PR of an equilateral triangle PQR. Show that PT < QT
In the given figure, T is a point on the side PR of an equilateral triangle PQR. Show that RT < QT
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.
