In Delta PQR,S is any point in its interior. | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(N/A) $1$. Extend $QS$ to meet $PR$ at point $T$.$2$. In $\Delta PQT$,by the triangle inequality theorem,the sum of two sides is greater than the thir

Vedclass · Accepted Answer

Vedclass · Answer

(N/A) $1$. Extend $QS$ to meet $PR$ at point $T$.
$2$. In $\Delta PQT$,by the triangle inequality theorem,the sum of two sides is greater than the third side: $PQ + PT > QT$. This can be written as $PQ + PT > QS + ST$ (Equation $1$).
$3$. In $\Delta SRT$,by the triangle inequality theorem,$ST + TR > SR$ (Equation $2$).
$4$. Adding Equation $1$ and Equation $2$: $PQ + PT + ST + TR > QS + ST + SR$.
$5$. Simplifying by canceling $ST$ from both sides: $PQ + (PT + TR) > QS + SR$.
$6$. Since $PT + TR = PR$,we get $PQ + PR > QS + SR$,which is equivalent to $SQ + SR < PQ + PR$.

In $\Delta PQR$,$S$ is any point in its interior. Prove that $SQ + SR < PQ + PR$.

Similar Questions

In $\Delta PQR$,$X$ is the midpoint of $QR$. $XY$ and $XZ$ are altitudes from $X$ on $PQ$ and $PR$ respectively. If $XY = XZ$,then prove that $\Delta PQR$ is an isosceles triangle.

If one angle of a triangle is equal to the sum of the other two angles,then the triangle is

In $\Delta ABC$,$\angle A : \angle B : \angle C = 5 : 7 : 8$. Find the measure of each angle of $\Delta ABC$.

$\angle PRT$ is an exterior angle of $\Delta PQR$. If $\angle P = 70^{\circ}$ and $\angle Q = 50^{\circ}$,then $\angle PRT = \ldots$ (in $^{\circ}$)

$ABC$ and $DBC$ are two isosceles triangles on the same base $BC$ (see figure). Show that $\angle ABD = \angle ACD$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module