Answer the following
1. In the figure below, ABC is a triangle in which AB = AC. X and Y are points on AB and AC such that AX = AY. Prove that ΔABY ≌ ΔACX
2. In a right angled triangle, one acute angle is double the other. Prove that the hypotenuse is double the smallest side.
3. In the given figure, triangles PQC and PRC are such that QC = PR and PQ = CR. Prove that ∠PCQ = ∠CPR.
4. 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.
5. 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
6. ABCD is a quadrilateral in which AD = BC and ∠DAB = ∠CBA (see Figure). Prove that
(i) ΔABD ≌ ΔBAC
(ii) BD = AC
(iii) ∠ABD = ∠BAC.
7. AB is a line segment and P is its mid-point. D and E are points on the same side of AB such that ∠BAD = ∠ABE and ∠EPA = ∠DPB (see figure). Show that
(i) ΔDAP ≌ ΔEBP
(ii) AD = BE
8. ABC and DBC are two isosceles triangles on the same base BC (see figure). Show that ∠ABD = ∠ACD.
9. Two sides AB and BC and median AM of one triangle ABC are respectively equal to sides PQ and QR and median PN of ΔPQR (see figure). Show that
(i) ΔABM ≌ ΔPQN (ii) ΔABC ≌ ΔPQR
10. In the adjoining figure, sides AB and AC of ΔABC are extended to points P and Q respectively. Also, ∠PBC < ∠QCB. Show that AC > AB.
11. AB and CD are respectively the smallest and longest sides of a quadrilateral ABCD (see figure). Show that ∠A > ∠C and ∠B > ∠D.
12. In the figure, PR > PQ and PS bisects ∠QPR. Prove that ∠PSR > ∠PSQ.
13. Show that of all line segments drawn from a given point not on it, the perpendicular line segment is the shortest.
Downloaded from https://qusaistuition.blogspot.com
(i) ΔDAP ≌ ΔEBP
(ii) AD = BE
8. ABC and DBC are two isosceles triangles on the same base BC (see figure). Show that ∠ABD = ∠ACD.
9. Two sides AB and BC and median AM of one triangle ABC are respectively equal to sides PQ and QR and median PN of ΔPQR (see figure). Show that
(i) ΔABM ≌ ΔPQN (ii) ΔABC ≌ ΔPQR
10. In the adjoining figure, sides AB and AC of ΔABC are extended to points P and Q respectively. Also, ∠PBC < ∠QCB. Show that AC > AB.
11. AB and CD are respectively the smallest and longest sides of a quadrilateral ABCD (see figure). Show that ∠A > ∠C and ∠B > ∠D.
12. In the figure, PR > PQ and PS bisects ∠QPR. Prove that ∠PSR > ∠PSQ.
13. Show that of all line segments drawn from a given point not on it, the perpendicular line segment is the shortest.
Downloaded from https://qusaistuition.blogspot.com
0 comments:
Post a Comment