7.9 TEST YOURSELF

7.9 TEST YOURSELF

1. PQRS is a quadrilateral in which PS = QR and SPQ = RQP. Prove that (i)   PQS  QPR (ii) QS = PR  (iii)  PQS = QPR.

 

 

 

2. Line ‘l’ is the bisector of M and N is any point on ‘l’. NA and NB are perpendiculars from N to the arms of M.

Show that

(i)   MAN  MBN

(ii)  NA = NB

 

 

3. State the S.A.S congruence rule.

4. PQR and SQR are two isosceles triangles on the same base QR.

Show that PQS = PRS.

 

 

 

 

 

 

5. In PQR, PS is the perpendicular bisector of OR, P

Show that  PQR is an isosceles

in which PQ = PR.

 

6. State the R.H.S congruence rule.

 

7. PQR and  SQR are two isosceles triangles on the same base QR and vertices P and S are on the same side of QR.  If PS is extended to intersect QR at T,then prove that

(i)   PQS  PRS

(ii)   PQT  PRT

(iii)  PT bisects P as well as S.

 

 

 

8. CM and RN are two equal altitudes of PQR.  Using R.H.S congruence rule prove that  PQR is isosceles.

 

9. In the fig. Q < P and R < S. Show that PS < QR.