Advertisements
Advertisements
प्रश्न
AD is a median of the triangle ABC. Is it true that AB + BC + CA > 2AD? Give reason for your answer.
Advertisements
उत्तर
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
संबंधित प्रश्न
In an isosceles triangle ABC, with AB = AC, the bisectors of ∠B and ∠C intersect each other at O. Join A to O. Show that:
- OB = OC
- AO bisects ∠A
Two lines AB and CD intersect at O such that BC is equal and parallel to AD. Prove that the lines AB and CD bisect at O.
In a ΔABC, if AB = AC and ∠B = 70°, find ∠A.
P is a point on the bisector of an angle ∠ABC. If the line through P parallel to AB meets BC at Q, prove that triangle BPQ is isosceles.
Fill the blank in the following so that the following statement is true.
Angle opposite to equal sides of a triangle are .....
Fill the blank in the following so that the following statement is true.
In right triangles ABC and DEF, if hypotenuse AB = EF and side AC = DE, then ΔABC ≅ Δ ……
Fill in the blank to make the following statement true.
The sum of three altitudes of a triangle is ..... than its perimeter.
Fill in the blank to make the following statement true.
The sum of any two sides of a triangle is .... than the third side.
In a triangle ABC, if AB = AC and AB is produced to D such that BD = BC, find ∠ACD: ∠ADC.
In the given figure, if AB ⊥ BC. then x =
In the given figure, what is z in terms of x and y?
In the given figure, for which value of x is l1 || l2?
In the given figure, AB and CD are parallel lines and transversal EF intersects them at Pand Q respectively. If ∠APR = 25°, ∠RQC = 30° and ∠CQF = 65°, then
The base BC of triangle ABC is produced both ways and the measure of exterior angles formed are 94° and 126°. Then, ∠BAC =
If the bisectors of the acute angles of a right triangle meet at O, then the angle at Obetween the two bisectors is
D is a point on the side BC of a ∆ABC such that AD bisects ∠BAC. Then ______.
Is it possible to construct a triangle with lengths of its sides as 8 cm, 7 cm and 4 cm? Give reason for your answer.
CDE is an equilateral triangle formed on a side CD of a square ABCD (Figure). Show that ∆ADE ≅ ∆BCE.
Bisectors of the angles B and C of an isosceles triangle ABC with AB = AC intersect each other at O. Show that external angle adjacent to ∠ABC is equal to ∠BOC
Show that in a quadrilateral ABCD, AB + BC + CD + DA < 2(BD + AC)
