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

In ΔABC, X and Y are two points on AB and AC such that AX = AY. If AB = AC, prove that CX = BY.

In the figure, AC = AE, AB = AD and ∠BAD = ∠EAC. Prove that BC = DE.

If the perpendicular bisector of the sides of a triangle PQR meet at I, then prove that the line joining from P, Q, R to I are equal.

In the given figure ABCD is a parallelogram, AB is Produced to L and E is a midpoint of BC. Show that:

a. DDCE ≅ DLDE
b. AB = BL
c. DC = `"AL"/(2)`

In the figure, ∠BCD = ∠ADC and ∠ACB =∠BDA. Prove that AD = BC and ∠A = ∠B.

In the figure, AP and BQ are perpendiculars to the line segment AB and AP = BQ. Prove that O is the mid-point of the line segments AB and PQ.

ΔABC is isosceles with AB = AC. BD and CE are two medians of the triangle. Prove that BD = CE.

Sides, AB, BC and the median AD of ΔABC are equal to the two sides PQ, QR and the median PM of ΔPQR. Prove that ΔABC ≅ ΔPQR.

Prove that in an isosceles triangle the altitude from the vertex will bisect the base.

In ΔABC, AB = AC. D is a point in the interior of the triangle such that ∠DBC = ∠DCB. Prove that AD bisects ∠BAC of ΔABC.

O is any point in the ΔABC such that the perpendicular drawn from O on AB and AC are equal. Prove that OA is the bisector of ∠BAC.

In ΔABC, AB = AC, BM and Cn are perpendiculars on AC and AB respectively. Prove that BM = CN.

ΔABC is an isosceles triangle with AB = AC. GB and HC ARE perpendiculars drawn on BC.

Prove that 
(i) BG = CH
(ii) AG = AH

In ΔABC, AD is a median. The perpendiculars from B and C meet the line AD produced at X and Y. Prove that BX = CY.

Two right-angled triangles ABC and ADC have the same base AC. If BC = DC, prove that AC bisects ∠BCD.

PQRS is a quadrilateral and T and U are points on PS and RS respectively such that PQ = RQ, ∠PQT = ∠RQU and ∠TQS = ∠UQS. Prove that QT = QU.

In the given figure, AB = DB and AC = DC. Find the values of x and y.

The mark obtained by the students in a class test are given below: 
31, 12, 28, 45, 32, 16, 49, 12, 18, 26, 34, 39, 29, 28, 25, 46, 32, 13, 14, 26, 25, 34, 23, 23, 25, 45, 33, 22, 18, 37, 26, 19, 20, 30, 28, 38, 42, 21, 36, 19, 20, 40, 48, 15, 46, 26, 23, 33, 47, 40.

Arrange the above marks in classes each with a class size of 5 and answer the following:
(i) what is the highest score?
(ii) What is the lowest score?
(iii) What is the range?
(iv) If the pass mark is 20, how many students failed/
(v) How many students got 40 or more marks?

The runs scored by a cricket player in the last 30 innings are:

75, 125, 36, 89, 154, 56, 12, 28, 96, 142, 78, 54, 30, 88, 116, 104, 55, 84, 10, 29, 31, 08, 24, 136, 117, 22, 99, 80, 112, 35.

Arrange these scores in an ascending order and answer the following:

1. Find the highest score.
2. Find the number of centuries scored by him.
3. Find the number of times he scored over 50.
4. Find the number of times he failed to score a 50.

Construct a grouped frequency table from the following data of the daily wages earned by 60 labourers in a company. Take each class size as 7.

25, 26, 34, 48, 39, 16, 55, 28, 37, 42, 45, 55, 28, 54, 53, 18, 35, 47, 44, 28, 55, 45, 39, 54, 21, 49, 45, 38, 29, 53, 48, 44, 15, 28, 14, 32, 15, 44, 14, 15, 16, 41, 33, 52, 29, 34, 51, 22, 19, 37, 44, 25, 48, 38, 24, 52, 51, 42, 32, 27.