In the diagram, $PQR$ and $QST$ are straight lines. It is given that $TQ$ is perpendicula

Question

In the diagram, $PQR$ and $QST$ are straight lines. It is given that $TQ$ is perpendicular to $PR$, $PT=SR$, $QR=2QS$, where $S$ is the midpoint of $QT$ and $\angle QRS=28{}^\circ$. Identify a pair of congruent triangles and state the reason for their congruence. If the length of $QS$ is $20$ units, find the ratio $PQ:QR$. Source check: in right triangle $QRS$, $QR=2QS$ implies $\tan\angle QRS=1/2$, so the angle is approximately $26.6^\circ$, not the printed $28^\circ$. The requested congruence proof and ratio use the side conditions and do not require that inconsistent angle.

Accepted Answer

$\text{(i)}\ \triangle TQP\equiv\triangle RQS\text{ (RHS)}$ $\text{(ii)}\ PQ:QR=1:2$ Results are conditional as explained in the source check; the complete printed givens are inconsistent.

Proving using RHS Congruency Test

Proving using RHS Congruency Test

Video Solution:

Solution:

Solution locked