(English Medium) ICSE Class 9 - CISCE Question Bank Solutions

The given figure shows a circle with center O. P is mid-point of chord AB.

Show that OP is perpendicular to AB.

The following figure shows a circle with center O.

If OP is perpendicular to AB, prove that AP = BP.

In a triangle ABC, D is mid-point of BC; AD is produced up to E so that DE = AD.
Prove that :
(i) ΔABD and ΔECD are congruent. 
(ii) AB = CE.
(iii) AB is parallel to EC

In a triangle ABC, D is mid-point of BC; AD is produced up to E so that DE = AD. Prove that:

 AB = CE.

In a triangle ABC, D is mid-point of BC; AD is produced up to E so that DE = AD. Prove that:

AB is parallel to EC.

A triangle ABC has ∠B = ∠C.
Prove that: The perpendiculars from the mid-point of BC to AB and AC are equal.

A triangle ABC has ∠B = ∠C.

Prove that: The perpendiculars from B and C to the opposite sides are equal.

The perpendicular bisectors of the sides of a triangle ABC meet at I.

Prove that: IA = IB = IC.

A line segment AB is bisected at point P and through point P another line segment PQ, which is perpendicular to AB, is drawn. Show that: QA = QB.

If AP bisects angle BAC and M is any point on AP, prove that the perpendiculars drawn from M to AB and AC are equal.

From the given diagram, in which ABCD is a parallelogram, ABL is a line segment and E is mid-point of BC.
Prove that: 
(i) ΔDCE ≅ ΔLBE 
(ii) AB = BL.
(iii) AL = 2DC

From the given diagram, in which ABCD is a parallelogram, ABL is a line segment and E is mid-point of BC.

Prove that: AB = BL.

From the given diagram, in which ABCD is a parallelogram, ABL is a line segment and E is mid-point of BC.

prove that : AL = 2DC

In the given figure, AB = DB and Ac = DC.

If ∠ ABD = 58^o,
∠ DBC = (2x - 4)^o,
∠ ACB = y + 15^o and
∠ DCB = 63^o ; find the values of x and y.

In the given figure: AB//FD, AC//GE and BD = CE;

prove that: 

1. BG = DF     
2. CF = EG   

In ∆ABC, AB = AC. Show that the altitude AD is median also.

In the following figure, BL = CM.

Prove that AD is a median of triangle ABC.

In the following figure, AB = AC and AD is perpendicular to BC. BE bisects angle B and EF is perpendicular to AB.

Prove that: BD = CD

In the following figure, AB = AC and AD is perpendicular to BC. BE bisects angle B and EF is perpendicular to AB.
Prove that :  ED = EF 

In the following figures, the sides AB and BC and the median AD of triangle ABC are equal to the sides PQ and QR and median PS of the triangle PQR.
Prove that ΔABC and ΔPQR are congruent.