Inequalities of a triangle - class-VIII
Description: inequalities of a triangle | |
Number of Questions: 47 | |
Created by: Ashok Pandey | |
Tags: congruence and inequalities of triangles triangle and its properties construction of parallel lines and triangles geometry inequalities maths triangles verification of the relation between the angles and sides of a triangle congruency of triangles |
If $O$ is any point in the interior of $\Delta ABC$. then "$2(OA+OB+OC)=(AB+BC+CA)$" the statement is?
In $\triangle {ABC},ABC,APQ$ and $\overline { PQ } \parallel \overline { BC } $. If $PQ=5,AP=4,AB=12$, then $BC=$_____
If a,b,c are the sides of a triangle ABC, then $\sqrt{a} + \sqrt{b} - \sqrt{c} $ is always:
In a $\Delta ABC$, side AB has the equation $2x+3y=29$ and the side AC has the equation, $x+2y=6$. If the mid-point of BC is (5, 6), then the equation of BC is
In a triangle ABC , if AB , BC and AC are the three sides of the triangle , then which of the following statements is necessarily true ?
For a triangle ABC, which of the following is true?
In $\triangle PQR$, if $\angle R\displaystyle>\angle Q$, then
The perimeter of a triangle is $.........$ than the sum of its medians.
In a right triangle, the hypotenuse is the $.......$ side
The sum of the three altitudes of a triangle is $......$ than its perimeter
Can $6$ cm, $5$ cm and $3$ cm form a triangle?
Two sides of a $\Delta$ le are $7$ and $10$ units. Which of the following length can be the length of the third side?
If a, b and c are the sides of a $\Delta$ le then
Which of the following statement is false?
If A is the area of a triangle in em", whose sides are 9 em, 10 cm and 11 em, then which one of the following is correct?
ABCD is a quadrilateral. Then which of the following is true?
Can 6 cm 5 cm and 3 cm form a triangle?
Two sides of a triangle have lengths $7$ and $9$. Which of the following could not be the length of the third side?
In a triangle, the difference of any two sides is ____ than the third side.
Which of the following sets of measurements can be used to construct a triangle?
Two sides of an acute-angled triangle are $6\ cm$ and $2\ cm$ respectively. Which one of the following represents the correct range of the third side in cm?
In $\Delta ABC, AD \bot BC; BE \bot AC; CF \bot AB.$ then which of the following option is correct:
In a $\Delta ABC$, which of the following relation is correct where A, B, C are the vertices and D, E, F are the corresponding mid-points?
The longest side of a triangle is three times the shortest side and the third side is $2$ cm shorter than the longest side. If the perimeter of the triangle is at least $61$ cm, find the minimum length of the shortest-side.
If the inequality $\left( m-2 \right) { x }^{ 2 }+8x+m+4>0$ is satisfied for all $x\epsilon R$, then least integral m is
Triangle ABC has integral sides AB, BC measuring $2001$ unit and $1002$ units respectively. Then the number of such triangles, is?
$O$ is any point in the interior of $\Delta ABC.$ then
$OA + OB + OC < \frac{1}{2}\left( {AB + BC + CA} \right)$ statement is ?
O if any point in the interior of a triangle ABC.
Which of the following will form the sides of a triangle?
The length of altitude through $A$ of the triangle $ABC$, where $A = (-3,\ 0);\ B = (4,\ -1);\ C = (5,\ 2).$
In triangle ABC, (a +b -c )(b+c -a)(c+a-b)-abc is always ;
In a triangle $ABC, \angle C=90^{o}, a=3, b=4$ and $D$ is a point on $AB$, so that $\angle BCD=30^{o}$. Then the length of $CD$ is
In a triangle $ABC, \angle ABC=50^{o}, \angle BAC=30^{o}$, then the shortest sides is
If two sides of a triangle are 8 cm and 13 cm, then the length of the third side is between a cm and b cm. Find the values of a and b such that a is less than b.
Two sides of a triangle are $7$ and $10$ units, which of the following length can be the length of the third side?
If AB > AC and length of median from C is 4 units, then the length of median from B can be
If $k$ is an integer and $2 < k < 7$, for how many different values of $k$ is there a triangle with sides of lengths $2, 7$, and $k$?
All equilateral triangles are ____.
Find the length of the third side of the triangle inequality, if sides of a triangle have $a = 4$ and $b = 8$.
In triangle $PQR$, an exterior angle at $A$ measures $160^o$, and $\angle$ $Q = 70 ^o$. Which is the longest side of the triangle?
Mark the triplet that can be the lengths of the sides of a triangle.
Two sides of a triangle have lengths $5$ and $8$, and the length of the third side is an integer. What is the greatest possible value of the perimeter of the triangle?
In a triangle $ABC$, $(a+b+c)(b+c-a)=k$$bc$ if:
$D$ is a point on the side $BC$ of a $\Delta$ $ABC$, such that $AD$ bisects $\angle $ $BAC$. Then:
Let a,b,c be the sides of a triangle. No two of them are equal and $\lambda \in R.$ If the roots of the equation
The area of the triangle formed by the lines $x ^ { 2 } - 3 x y + y ^ { 2 } = 0$ and $x + y + 1 = 0$ is square units. is
In a triangle ABC. The relation which is true for its sides is-