Chapter 7.2, Problem 4PSA

To determine

To prove : The congruency of $\Delta RKM\cong \Delta OMK$ .

Explanation of Solution

Given information : The following information has been given

  $\angle MRK=\angle KOM={90}^0$

  $\angle RKM=\angle OMK$

KM is the common chord

Formula used : By the virtue of similarity, if any two angles of the triangles are congruent, the third one will also be congruent

Proof : We know that in triangles RKM and OMK,

  $\angle MRK=\angle KOM={90}^0$

  $\angle RKM=\angle OMK$

KM is the common chord

Hence, by virtue of similarity,

  $\angle RMK=\angle OKM$

Now, we can say that $\Delta RKM\cong \Delta OMK$ by SAS property of congruency

Hence, given congruency is proved