In Delta PQR, the bisector of angle P interse | vedclass

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(A) According to the Angle Bisector Theorem, the bisector of an angle of a triangle divides the opposite side into segments that are proportional to t

Vedclass · Accepted Answer

$7$

Vedclass · Answer

(A) According to the Angle Bisector Theorem, the bisector of an angle of a triangle divides the opposite side into segments that are proportional to the other two sides of the triangle.In $\Delta PQR$, since $PS$ is the bisector of $\angle P$, we have the ratio: $\frac{PQ}{PR} = \frac{QS}{SR}$.Given $QR = 9.6$ and $QS = 4$, we can find $SR$ as: $SR = QR - QS = 9.6 - 4 = 5.6$.Substituting the known values into the theorem: $\frac{5}{PR} = \frac{4}{5.6}$.Cross-multiplying gives: $4 	imes PR = 5 	imes 5.6$.$4 	imes PR = 28$.$PR = \frac{28}{4} = 7$.Therefore, the length of $PR$ is $7$.

Part $I$	Part $II$
$1.$ In $\Delta ABC$,$\angle B$ is a right angle and $\overline{BM}$ is a median.	$a. AB^2 + BC^2 = 2(BD^2 + CD^2)$
$2.$ In $\Delta ABC$,$\angle A$ is a right angle and $\overline{AD}$ is an altitude.	$b. BC = \frac{1}{2} AB$
$3.$ In $\Delta ABC$,$m\angle C = 90^\circ$ and $m\angle A = 30^\circ$.	$c. AC^2 = CD \cdot BC$
$4.$ In $\Delta ABC$,$\overline{BD}$ is a median.	$d. BM = \frac{1}{2} AC$

In $\Delta PQR$, the bisector of $\angle P$ intersects $\overline{QR}$ at $S$. If $PQ = 5$, $QS = 4$ and $QR = 9.6$, find $PR$.

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