In quadrilateral $ABCD,$ side $AB$ is the longest and side $DC$ is the shortest.
Prove that$: D >B.$
View full solution →Prove that$: D >B.$
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Inequalities questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
In the following figure$, A B C$ is an equilateral triangle and $P$ is any point in $A C;$
prove that $: BP > PC$
View full solution →prove that $: BP > PC$
In the following figure $, A B C$ is an equilateral triangle and $P$ is any point in $AC;$
prove that $: BP > PA$
View full solution →prove that $: BP > PA$
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 $b.$
View full solution →In $\triangle ABC, \text{AB} > \text{AC}$ and $D$ is a point inside $\text{BC}$.Show that$: \text{AB} > \text{AD}.$
View full solution →Given: $\text{ED} = \text{EC}$, Prove: $\text{AB}+\text{AD}>\text{BC}$.
View full solution →In $\triangle ABC,$ side $\text{AC}$ is greater than side $\text{AB}$. If the internal bisector of angle $A$ meets the opposite side at point $D$,prove that$: \angle ADC$ is greater than $\angle ADB.$
View full solution →In quadrilateral $\text{ABCD},$ side $\text{AB}$ is the longest and side $\text{DC}$ is the shortest.Prove that$: C > A.$
View full solution →$D$ is a point in side $BC$ of $\triangle ABC.$ If $AD > AC$, show that $AB > AC.$
View full solution →In the following figure, write $BC , AC$, and $CD$ in ascending order of their lengths.
View full solution →In a $\triangle P Q R ; Q R=P R$ and $\angle P=36^{\circ}$. Which is the largest side of the triangle?
View full solution →The sides$ AB$ and $AC$ of a $\triangle ABC$ are produced; and the bisectors of the external angles at $B$ and $C$ meet at $P.$Prove that if $AB > AC,$ then $PC > PB.$
View full solution →Prove that the straight line joining the vertex of an isosceles triangle to any point in the base is smaller than either of the equal sides of the triangle.
From the following figure;
prove that:$(i) AB > BD;(ii) A C>C D;(iii) A B+A C>B C$.A
View full solution →prove that:$(i) AB > BD;(ii) A C>C D;(iii) A B+A C>B C$.A
In the following figure $; A C=C D ; \angle B A D=110^{\circ}$ and $\angle A C B=74^{\circ}$.
Prove that: $BC > CD$.
View full solution →Prove that: $BC > CD$.
In the following figure, $\angle B A C=60^{\circ}$ and $\angle A B C=65^{\circ}$.
Prove that:$(i) CF > AF;(ii)DC > DF$
View full solution →Prove that:$(i) CF > AF;(ii)DC > DF$
Arrange the sides of $\triangle BOC$ in descending order of their lengths. $BO$ and $C O$ are bisectors of angles $\text{ABC}$ and $\text{ACB}$ respectively.
View full solution →In the following figure, write $BC , AC$, and $CD$ in ascending order of their lengths.
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