Triangles-HOTS Questions

1.  ABCD is a quadrilateral in which AD = BC and ∠DAB = ∠CBA. Prove that δABD ≌ ΔBAC.

2.  In the given figure, triangles PQC and PRC are such that QC = PR and PQ = CR. Prove that ∠PCQ = ∠CPR.

3.  In the given figure, AB = AD, AC = AE and ∠BAD = ∠EAC, then prove that BC = DE.

4.  ΔPQR is given and the sides QP and RP have been produced to S and T such that PQ = PS and PR = PT. Prove that the segment QR || ST.

5.  In the given figure, AB = BC and ∠ABO = ∠CBO, then prove that ∠DAB = ∠ECB.

6.  In the given figure, AD is bisector of ∠BAC and ∠CPD = ∠BPD. Prove that ΔCAP ≌ ΔBAP.

7.  In the given figure, PS is median produced upto F and QE and RF are perpendiculars drawn from Q and R, prove that QE = RF.

8.  In the given figure, equilateral ΔABD and ΔACE are drawn on the sides of a ΔABC. Prove that CD = BE.

9.  In given figure, RS is diameter and PQ chord of a circle with centre O. Prove that (a) ∠RPO = ∠OQR (b) ∠POQ = 2∠PRO

10.  In the given figure, T and M are two points inside a parallelogram PQRS such that PT = MR and PT || MR. Then prove that

      (a) ΔPTR ≌ ΔRMP

      (b) RT || PM and RT = RM