Question

guys one question help me plezzz fast??​

Answer 1

$\large\underline{\sf{Given- }}$

$\rm \: \angle B \: < \: \angle A$

and

$\rm \: \angle C \: < \: \angle D$

$\purple{\large\underline{\sf{To\:show - }}}$

$\rm \: AD \: < \: BC$

$\green{\large\underline{\sf{Solution-}}}$

In triangle AOB

It is given that

$\rm \: \angle B \: < \: \angle A$

$\rm\implies \:\angle A \: > \: \angle B$

We know,

Side opposite to greater angle is always longest.

$\rm\implies \:\boxed{\tt{ \: \: OB \: > \: OA}} - - - (1)$

Now, In triangle COD

It is given that

$\rm \: \angle C \: < \: \angle D$

$\rm\implies \:\angle D \: > \: \angle C$

We know,

Side opposite to greater angle is always longest.

$\rm\implies \: \: \boxed{\tt{ \: \: OC \: > \: OD \: }} \: - - - - (2)$

On adding equation (1) and (2), we get

$\rm \: OB + OC > OA + OD$

$\rm\implies \:BC \: > \: AD$

$\rm\implies \:AD \: < \: BC$

Hence, Proved

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ADDITIONAL INFORMATION

1. If two sides of a triangle are unequal, the smallest side has smaller angle opposite to it.

2. If two sides of a triangle are unequal, the longest side has greater angle opposite to it.

3. The sum of any two sides of a triangle is greater than the third side.

4. The exterior angle of a triangle is equals to sum of interior opposite angles.

5. The sum of all interior angles of a triangle is supplementary.

6. If altitudes of a triangle are equal, then triangle is equilateral triangle.

Answer 2

$\boxed{ \large{ \underline{ \gray{ \sf \: solution}}}}$

= Angle B < Angle A

= Angle A > Angle B

Opposite to greater angle is always longest.

OB > OA -----------(1)

Now,

Angle C < Angle D

= Angle D > Angle C

Then,

OC > OD -----------(2)

Adding equation (1) and (2)

= OB + OC > OA + OD

= BC > AD

= AD < BC