Question

In the figure PS is median produced up to F and QE and RF are perpendiculars drawn from Q and R prove that QE=RF

Answer 1

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Answer 2

Answer:

Applying rules of triangle, proved that QE=RF.

Step-by-step explanation:

Given PS is median produced up to F.

QE and RF are perpendiculars drawn from Q and R.

If PS is the median, then QS is equal to RS i.e., $\overline {QS}=\overline{RS}$

And from the perpendiculars, we get $\angle QES=\angle RFS=90^o$

In the triangles QES  and RFS, QR and PF are intersecting lines.

∠QSE and ∠RSF are vertically opposite angles, and the measures of vertically opposite angles are equal.

$\angle QSE = \angle RSF$

From the Angle-Angle-Side(AAS) rule, two triangles are said to be congruent when two angles and a non-included side of two triangles are equal.

Therefore, $\triangle QES\cong \triangle RFS$  

Applying the corresponding parts of congruent triangles(CPCT) rule, if two triangles are congruent, then all their corresponding angles and sides are equal.        

We get $QE=RF$

Hence proved.