Advertisements
Advertisements
Question
D is a point on the side of the BC of ΔABC. Prove that the perimeter of ΔABC is greater than twice of AD.
Solution
Construction: Join AD
In triangle ACD,
AC + CD > AD ...(i)
(Sum of two of a triangle greater than the third side)
Similarly, in triangle ADB,
AB + BD > AD ...(ii)
Adding (i) and (ii),
AC + CD + AB + BD > AD
AB + BC + AC > 2AD. ...(Since, CD + BD = BC)
APPEARS IN
RELATED QUESTIONS
Show that of all line segments drawn from a given point not on it, the perpendicular line segment is the shortest.
Complete the hexagonal and star shaped rangolies (see the given figures) by filling them with as many equilateral triangles of side 1 cm as you can. Count the number of triangles in each case. Which has more triangles?
In the following figure ; AC = CD; ∠BAD = 110o and ∠ACB = 74o.
Prove that: BC > CD.
"Caste inequalities are still prevalent in India." Examine the statement.
Name the greatest and the smallest sides in the following triangles:
ΔDEF, ∠D = 32°, ∠E = 56° and ∠F = 92°.
In the given figure, ∠QPR = 50° and ∠PQR = 60°. Show that : PN < RN
In ΔPQR, PS ⊥ QR ; prove that: PQ > QS and PQ > PS
In ΔPQR, PS ⊥ QR ; prove that: PQ + PR > QR and PQ + QR >2PS.
In the given figure, T is a point on the side PR of an equilateral triangle PQR. Show that PT < QT
In ΔPQR is a triangle and S is any point in its interior. Prove that SQ + SR < PQ + PR.
