7.8 TEST YOURSELF.

7.8    TEST YOURSELF:

 

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

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)  ΔMAN ≅  ΔMBN

(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  ΔPQS  =  ΔPRS.

 

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

Show that ΔPQR is an isosceles triangle   in which PQ = PR.

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

 

7. ΔPQR and ΔSQR 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)  Δ PQS   ≅  ΔPRS

(ii)  ΔPQT   ≅  ΔPRT

(iii)  PT bisects P as well as S.

 

 

 

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

 

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