[2 Mark Question Answer]

Question 12 Marks

In quadrilateral $ABCD,$ side $AB$ is the longest and side $DC$ is the shortest.
Prove that$: D >B.$

Answer

$ \angle 5>\angle 6[A B>A D]$
$ \angle 3>\angle 8[B C>C D]$
$ \therefore \angle 5+\angle 3>\angle 6+\angle 8$
$ \Rightarrow \angle D>\angle B$

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Question 22 Marks

In the following figure$, A B C$ is an equilateral triangle and $P$ is any point in $A C;$
prove that $: BP > PC$

Answer

In $\triangle BPC,$
$\angle C = 60^\circ$
$\angle CBP < 60^\circ$
$\therefore \angle C > \angle CBP$
$\Rightarrow BP > PC ....[$ Side opposite to greater side is greater $]$

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Question 32 Marks

In the following figure $, A B C$ is an equilateral triangle and $P$ is any point in $AC;$
prove that $: BP > PA$

Answer

In $\triangle ABC$,
$A B=B C=C A ... [ ABC$ is an equilateral triangle $]$
$ \therefore \angle A=\angle B=\angle C$
$ \therefore \angle A=\angle B=\angle C=\frac{180^{\circ}}{3}$
In $\triangle ABP$,
$ \angle A =60^{\circ}$
$ \angle ABP <60^{\circ}$
$ \therefore \angle A >\angle ABP $
$\Rightarrow BP > PA ....[$ Side opposite to greater side is greater $]$

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MATHEMATICS [2 Mark Question Answer]

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