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

Construct a triangle using the following data: DE + EF = 10.3 cm, EF = 6.4 cm and ∠E = 75°

Construct a triangle using the given data: PQ - PR = 1.5 cm, QR = 6.0 and ∠Q = 45°

Construct a triangle using the given data: AB - AC = 1.2 cm, BC = 6.0 cm and ∠B = 60°

Construct a triangle using the given data: XY - XZ = 1.5 cm, YZ = 3.4 cm and ∠X = 45°

Construct a triangle using the given data: Perimeter of triangle is 6.4 cm, and the base angles are 60° and 45°

Construct a triangle using the given data: Perimeter of triangle is 9 cm, and the base angles are 60° and 45°

Construct a triangle using the given data: Perimeter of triangle is 10.6 cm, and the base angles are 60° and 45°

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.