Inequalities In A Triangle Free Doubts and Solutions
CBSE - IX - Mathematics - Triangles
Solve question no. 75

CBSE - IX - Mathematics - Triangles
Please solve question no. 60

CBSE - IX - Mathematics - Triangles
ABC is a triangle in which LB=2LC. D is a point on BC such that AD bisects LBAC and AB=CD. Prove that LBAC=72 degree.
CBSE - IX - Mathematics - Triangles
In a right angled triangle, one acute angle is double the other. Then the hypotenuse is 'k'times the smallest side. The k=?
CBSE - IX - Mathematics - Triangles
Prove that the sum of the three altitudes of a triangle is less than the sum of the three sides of the triangle.
CBSE - IX - Mathematics - Triangles
In the figure AD is the bisector of A, prove that AB > BD.
CBSE - IX - Mathematics - Triangles
Show that of all line segment drawn from a given point not on it, the perpendicular line segment is the shortest.
CBSE - IX - Mathematics - Triangles
There is a triangular field ABC whose corner angles A, B and C have been measured as 50o, 60o and 70o respectively. Three friends Rashmi, Salma and Arun daily go on morning walk and respectively walk along AB, BC and AC. Who walks maximum distance among these three? Who walks the least? What value is indicated from this action?
CBSE - IX - Mathematics - Triangles
In fig., if a > b then prove that PQ > PR.
CBSE - IX - Mathematics - Triangles
In a ΔDEF, if D = 30° E = 60° then which side of the triangle is longest and which side is shortest?
CBSE - IX - Mathematics - Triangles
In fig., D is any point on the base BC produced of an isosceles triangle ABC. Prove that AD > AB.
CBSE - IX - Mathematics - Triangles
In the given figure, ABD = 130° and EAC = 120°. Prove that AB > AC.
CBSE - IX - Mathematics - Triangles
In figure , AB > AC, BO and CO are the bisectors of B and C respectively. Show that OB > OC.
CBSE - IX - Mathematics - Triangles
In fig., PR > PQ and PS bisects QPR. Prove that PSR > PSQ.
CBSE - IX - Mathematics - Triangles
Show that in a right angled triangle the hypotenuse is the longest side.
CBSE - IX - Mathematics - Triangles
In figure, D is a point on side BC of such that AD=AC. Show AB>AD.
CBSE - IX - Mathematics - Triangles
Prove that the sum of any two sides of a triangle is greater than twice the length of median drawn to the third side.
CBSE - IX - Mathematics - Triangles
In figure, show that 2 (AC + BD) > (AB + BC + CD + DA)
CBSE - IX - Mathematics - Triangles
The side BC of ABC is produced on both sides. Prove that the sum of the two exterior angles so formed is greater than A by 180o.
CBSE - IX - Mathematics - Triangles
If AD is the bisector of A of ABC, show that AB > DB.
CBSE - IX - Mathematics - Triangles
In figure, AB and CD are respectively the smallest and the longest sides of a quadrilateral ABCD, then show that A > C and B > D.
CBSE - IX - Mathematics - Triangles
In triangle ABC, D is a point on AC, Prove that, the value of the perimeter of triangle ABC is greater than twice the length of BD.
CBSE - IX - Mathematics - Triangles
Prove that diagonals of a rectangle are equal but not perpendicular.
CBSE - IX - Mathematics - Triangles
The sides of AB, BC, AC a triangle ABC are 2.8 cm, 3.7 cm and 4.1 cm respectively. What is the relationship between the angles A, B, and C?
CBSE - IX - Mathematics - Triangles
Prove that if the median AD of a triangle ABC is greater than half of BC, then,
CBSE - IX - Mathematics - Triangles
In triangle ABC, AB = BC; angle B is half of angle A. Is AB > AC? Give reason for your answer.
CBSE - IX - Mathematics - Triangles
In a triangle ABC, AB = 3 cm, BC = 3.5 cm and CA = 6.5 cm. Is it possible to construct this triangle? Give reason for your answer.
CBSE - IX - Mathematics - Triangles
Prove that in a right triangle, the hypotenuse is the longest side.
CBSE - IX - Mathematics - Triangles
In the figure PQ > PR, QS and RS are the bisectors of Q and R respectively. Prove that SQ > SR.
CBSE - IX - Mathematics - Triangles
Prove that if two sides of a triangle are unequal, the longer side has greater angle opposite it.
CBSE - IX - Mathematics - Triangles
Prove that the perimeter of a triangle is greater than the sum of its three medians.
CBSE - IX - Mathematics - Triangles
In the given figure, x > y. Show that LM > LN.
CBSE - IX - Mathematics - Triangles
Can you give me some difficult prove that questions with its solution ?
CBSE - IX - Mathematics - Triangles
Show that the sum of the three altitudes of a triangle is less than the sum of three sides of the triangle.
CBSE - IX - Mathematics - Triangles
In a triangle, prove that the greater angle has the longer side opposite to it
CBSE - IX - Mathematics - Triangles
In a right angled triangle, one acute angle is double the other. Then the hypotenuse is _______.
(A) Double the smallest side
(B) Thrice the smallest side
(C) 4 times the smallest side
(D) None
CBSE - IX - Mathematics - Triangles
O is any point in the interior of a triangle ABC then AB + AC is _________.
O is any point in the interior of a triangle ABC then AB + AC is _________.
CBSE - IX - Mathematics - Triangles
In triangle ABC, AD is the median. Then AB + AC is _________.
CBSE - IX - Mathematics - Triangles
<div>If I is the incentre of<img class="Wirisformula" src="https://images.topperlearning.com/topper/tinymce/integration/showimage.php?formula=6652abdbffb74104943625e3253daf18.png" alt="increment A B C" align="middle" /> and AI is produced to meet BC at X , then AI :IX = ?</div>
CBSE - IX - Mathematics - Triangles
P, Q and R are respectively , the midpoints of sides BC, CA and AB of a triangle ABC. PR and BQ meets X. CR and PQ meet at Y. Prove that XY = 1/4 BC
P, Q and R are respectively , the midpoints of sides BC, CA and AB of a triangle ABC. PR and BQ meets X. CR and PQ meet at Y. Prove that XY = 1/4 BC
CBSE - IX - Mathematics - Triangles
If sin A + sin B + sin C = 3, find cos A + cos B + cos C.
CBSE - IX - Mathematics - Triangles
In triangle ABC , I is the incentre. If angles BIC:CIA:AIB = 5 : 6 : 7 ,Then the value of angles A : B: C is:
CBSE - IX - Mathematics - Triangles
if AB=CB, AB=CD, and EF bisects BD at G .prove that G is mid point of EF
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