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

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.

ABCD is a parallelogram. The sides AB and AD are produced to E and F respectively, such produced to E and F respectively, such that AB = BE and AD = DF.

Prove that: ΔBEC ≅ ΔDCF.

In the parallelogram ABCD, the angles A and C are obtuse. Points X and Y are taken on the diagonal BD such that the angles XAD and YCB are right angles.
Prove that: XA = YC.

In the adjoining figure, QX and RX are the bisectors of the angles Q and R respectively of the triangle PQR.
If XS ⊥ QR and XT ⊥  PQ;

Prove that:

1. ΔXTQ ≅ ΔXSQ.
2. PX bisects angle P.

In a ΔABC, BD is the median to the side AC, BD is produced to E such that BD = DE.
Prove that: AE is parallel to BC.

In the figure, given below, triangle ABC is right-angled at B. ABPQ and ACRS are squares.

Prove that: 
(i) ΔACQ and ΔASB are congruent.
(ii) CQ = BS.

In the following diagram, ABCD is a square and APB is an equilateral triangle.

1. Prove that: ΔAPD ≅ ΔBPC
2. Find the angles of ΔDPC.

In the following diagram, AP and BQ are equal and parallel to each other.
Prove that: AB and PQ bisect each other.