English Medium कक्षा ९ - CBSE Question Bank Solutions for Mathematics

The following statement are true  and false .

If three sides of a quadrilateral are equal, it is a parallelogram .

The following statement are true  and false . 

If three angles of a quadrilateral are equal, it is a parallelogram .

The following statement are true  and false . 

If all the sides of a quadrilateral are equal it is a parallelogram.

Two parallel side of a trapezium are 60 cm and 77 cm and other sides are 25 cm and 26 cm. Find the area of the trapezium.

Find the area of a rhombus whose perimeter is 80 m and one of whose diagonal is 24 m.

Find the area of a quadrilateral ABCD in which AD = 24 cm, ∠BAD = 90° and BCD forms an equilateral triangle whose each side is equal to 26 cm. (Take √3 = 1.73)

Find the perimeter and area of the quadrilateral ABCD in which AB = 17 cm, AD =9 cm, CD = l2cm, ∠ACB = 90° and AC=l5cm.

In the given below fig. ABCD, ABFE and CDEF are parallelograms. Prove that ar (ΔADE)
= ar (ΔBCF)

A line segment AB is of length 5 cm. Draw a circle of radius 4 cm passing through A and B. Can you draw a circle of radius 2 cm passing through A and B? Give reason in support of your answer.

ABCD is a parallelogram, G is the point on AB such that AG = 2 GB, E is a point of DC
such that CE = 2DE and F is the point of BC such that BF = 2FC. Prove that:

(1)  ar ( ADEG) = ar (GBCD)

 (2)  ar (ΔEGB) = `1/6` ar (ABCD)

 (3)  ar (ΔEFC) = `1/2` ar (ΔEBF)

 (4)  ar (ΔEBG)  = ar (ΔEFC)

 ⁽⁵⁾ΔFind what portion of the area of parallelogram is the area of EFG.

The lengths of two parallel chords of a circle are 6 cm and 8 cm. if the smaller chord is at a distance of 4 cm from the centre, what is the distance of the other chord from the centre?

Three girls Ishita, Isha and Nisha are playing a game by standing on a circle of radius 20 m drawn in a park. Ishita throws a ball o Isha, Isha to Nisha and Nisha to Ishita. If the distance between Ishita and Isha and between Isha and Nisha is 24 m each, what is the distance between Ishita and Nisha.

In the below fig. ABCD and AEFD are two parallelograms. Prove that
(1) PE = FQ
(2) ar (Δ APE) : ar (ΔPFA) = ar Δ(QFD) : ar (Δ PFD)
(3) ar (ΔPEA) = ar (ΔQFD)

In Fig. 10.40, it is given that RT = TS, ∠1 = 2∠2 and ∠4 = 2∠3. Prove that ΔRBT ≅ ΔSAT. 

In Fig. 10.92, it is given that AB = CD and AD = BC. Prove that ΔADC ≅ ΔCBA. 

If perpendiculars from any point within an angle on its arms are congruent, prove that it lies on the bisector of that angle.  

In Fig. 10.99, AD ⊥ CD and CB ⊥. CD. If AQ = BP and DP = CQ, prove that ∠DAQ = ∠CBP. 

ABCD is a square, X and Yare points on sides AD and BC respectively such that AY = BX. Prove that BY = AX and ∠BAY = ∠ABX. 

Construct a ΔABC in which BC = 3.6 cm, AB + AC = 4.8 cm and ∠B = 60°.

Construct a ΔABC in which AB + AC = 5.6 cm, BC = 4.5 cm, AB − AC = 1.5 cm and ∠B = 45°.