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

Construct a ΔXYZ with YZ = 7.5 cm, ∠Y = 60° and ∠Z = 45°. Draw the bisectors of ∠Y and ∠Z. If these bisectors meet at O, measure angle YOZ.

Construct a triangle PQR with PQ = 5.4 cm, QR = 4.6 cm and ∠Q = 60°. Draw the perpendicular PS at QR, measure the lengths of SP and SQ,

Construct a ΔRST with side ST = 5.4 cm, RST = 60° and the perpendicular from R on ST = 3.0 cm.

Construct a ΔPQR with ∠Q = 60°, ∠R = 45° and the perpendicular from P to QR be 3.5 cm. Measure PQ.

Construct a ΔABC, right-angled at B with a perimeter of 10 cm and one acute angle of 60°.

In ΔABC, D is the mid-point of AB and E is the mid-point of BC.

Calculate:
(i) DE, if AC = 8.6 cm
(ii) ∠DEB, if ∠ACB = 72°

In ΔABC, AB = 12 cm and AC = 9 cm. If M is the mid-point of AB and a straight line through M parallel to AC cuts BC in N, what is the length of MN?

In ΔABC, D, E, F are the midpoints of BC, CA and AB respectively. Find FE, if BC = 14 cm

In ΔABC, D, E, F are the midpoints of BC, CA and AB respectively. Find DE, if AB = 8 cm

In ΔABC, D, E, F are the midpoints of BC, CA and AB respectively. Find ∠FDB if ∠ACB = 115°.

In parallelogram PQRS, L is mid-point of side SR and SN is drawn parallel to LQ which meets RQ produced at N and cuts side PQ at M. Prove that M is the mid-point of PQ.

In ΔABC, BE and CF are medians. P is a point on BE produced such that BE = EP and Q is a point on CF produced such that CF = FQ. Prove that: QAP is a straight line.

In ΔABC, BE and CF are medians. P is a point on BE produced such that BE = EP and Q is a point on CF produced such that CF = FQ. Prove that: A is the mid-point of PQ.

Prove that the figure obtained by joining the mid-points of the adjacent sides of a rectangle is a rhombus.

D, E and F are the mid-points of the sides AB, BC and CA of an isosceles ΔABC in which AB = BC. Prove that ΔDEF is also isosceles.

Prove that the straight lines joining the mid-points of the opposite sides of a quadrilateral bisect each other.

The diagonals of a quadrilateral intersect each other at right angle. Prove that the figure obtained by joining the mid-points of the adjacent sides of the quadrilateral is a rectangle.

If L and M are the mid-points of AB, and DC respectively of parallelogram ABCD. Prove that segment DL and BM trisect diagonal AC.

In a right-angled triangle ABC. ∠ABC = 90° and D is the midpoint of AC. Prove that BD = `(1)/(2)"AC"`.

In parallelogram ABCD, P is the mid-point of DC. Q is a point on AC such that CQ = `(1)/(4)"AC"`. PQ produced meets BC at R. Prove that

(i) R is the mid-point of BC, and

(ii) PR = `(1)/(2)"DB"`.