Advertisements
Advertisements
Question
AD is a median of the triangle ABC. Is it true that AB + BC + CA > 2AD? Give reason for your answer.
Advertisements
Solution
In triangle ABD,
AB + BD > AD ...(i)
AC + CD > AD ...(ii) [Sum of the length of any two sides of a triangle must be greater must be greater that the third side]
Adding (i) and (ii), we get
AB + BD + CD + AC > 2AD
AB + BC + CA > 2AD ...[BD = CD as AD is median of triangle ABC]
APPEARS IN
RELATED QUESTIONS
Determine the measure of each of the equal angles of a right-angled isosceles triangle.
AB is a line seg P and Q are points on opposite sides of AB such that each of them is equidistant from the points A and B (See Fig. 10.26). Show that the line PQ is perpendicular bisector of AB.
In a ΔABC, if ∠A=l20° and AB = AC. Find ∠B and ∠C.
In Figure 10.24, AB = AC and ∠ACD =105°, find ∠BAC.
In a ΔPQR, if PQ = QR and L, M and N are the mid-points of the sides PQ, QR and RP
respectively. Prove that LN = MN.
Fill the blank in the following so that the following statement is true.
Sides opposite to equal angles of a triangle are ......
In Fig. 10.131, prove that: (i) CD + DA + AB + BC > 2AC (ii) CD + DA + AB > BC
Which of the following statements are true (T) and which are false (F)?
Sum of the three sides of a triangle is less than the sum of its three altitudes.
Which of the following statements are true (T) and which are false (F)?
Difference of any two sides of a triangle is equal to the third side.
Which of the following statements are true (T) and which are false (F)?
Of all the line segments that can be drawn from a point to a line not containing it, the perpendicular line segment is the shortest one.
Fill in the blank to make the following statement true.
The sum of any two sides of a triangle is .... than the third side.
Fill in the blank to make the following statement true.
Difference of any two sides of a triangle is........ than the third side.
In the given figure, if AB || DE and BD || FG such that ∠FGH = 125° and ∠B = 55°, find x and y.
In the given figure, x + y =
If the measures of angles of a triangle are in the ratio of 3 : 4 : 5, what is the measure of the smallest angle of the triangle?
In the given figure, what is y in terms of x?
In ∆PQR, if ∠R > ∠Q, then ______.
In triangles ABC and PQR, AB = AC, ∠C = ∠P and ∠B = ∠Q. The two triangles are ______.
M is a point on side BC of a triangle ABC such that AM is the bisector of ∠BAC. Is it true to say that perimeter of the triangle is greater than 2 AM? Give reason for your answer.
CDE is an equilateral triangle formed on a side CD of a square ABCD (Figure). Show that ∆ADE ≅ ∆BCE.
