Class 9 Practice – Level 3 – Set 1 – Quadrilaterals

Total questions: 15

The bisectors of angles of a parallelogram form a rectangle.

Topic: Angle Bisectors in Parallelograms

Yes

None

ABCD is a parallelogram in which P and Q are mid-points of opposite sides AB and CD (see Fig. 8.18). If AQ intersects DP at S and BQ intersects CP at R, show that:

Topic: Properties of a Parallelogram

(i) APCQ is a parallelogram.
(ii) DPBQ is a parallelogram.
(iii) PSQR is a parallelogram.

True

False

None

K, L, M and N are points on the sides AB, BC, CD and DA respectively of a square ABCD such that AK = BL = CM = DN. The KLMN is a square.

Topic: Properties of a Square

True

False

Sometimes false

None of the above

None

PQRS is a trapezium in which PQ∣∣SR and M is the midpoint of PS. A line segment MN∣∣PQ meets QR at N the N is the midpoint of QR.

Topic: Properties of Trapezium

True

False

None

In a parallelogram ABCD,E and F are the mid-points of sides AB and CD respectively (see Fig). Show that the line segments AF and EC trisect the diagonal BD.

Topic: Properties of a Parallelogram

BQ = QP = PD

QP = PD = QB

PD = BQ = DP

None of the above

None

ABC is a triangle right angled at C. A line through the mid-point M of hypotenuse AB and parallel to BC intersects AC and D. Show that

Topic: Properties of Right-Angled Triangle

(i) D is the mid-point of AC (ii) MB⊥AC (iii) CM = MA =$ \displaystyle \dfrac{1}{2}$ AB

True

False

None

Show that the diagonals of a rhombus are perpendicular to each other.

Topic: Properties of Rhombus

Yes

None

ABCD is a square and △EDC is an equilateral triangle. Prove that

Topic: Properties of Squares and Equilateral Triangles

(i) AE = BE (ii) ∠DAE = 15°

Right

Wrong

None

Each side of a rhombus is 10cm long and one of its diagonals measures 16cm. Find the length of the other diagonal and hence find the area of the rhombus.

Topic: Diagonals and Area of a Rhombus

103$ \displaystyle c{{m}^{2}}$

96$ \displaystyle c{{m}^{2}}$

46$ \displaystyle c{{m}^{2}}$

58$ \displaystyle c{{m}^{2}}$

None

10.

The each angle of a rectangle is a right angle.

Topic: Properties of Rectangle

True

False

None

11.

In the figure, M is the midpoint of side BC of a parallelogram ABCD such that ∠BAM = ∠DAM. Then the AD = 2CD

Topic: Properties of a Parallelogram

Right

Wrong

None

12.

A △ABC is given. If lines are drawn through AB, B, C parallel respectively to the sides BC, CA and AB forming △PQR, as that the BC = $ \displaystyle \dfrac{1}{2}$ QR

Topic: Similarity of Triangles

Yes

None

13.

The diagonals of a quadrilateral ABCE are equal. The quadrilateral formed by joining the midpoints of its sides is a rhombus.

Topic: Properties of a Quadrilateral

True

False

None

14.

the quadrilateral formed by joining the midpoints of the pairs of adjacent sides of a rhombus is a rectangle.

Topic: Properties of Rhombus

True

False

None

15.

AD is a median of △ABC and DE∥BA. The BE is also a median of △ABC.

Topic: Median in a Triangle

True

False

None

1 out of 15

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Class 9 Practice – Level 3 – Set 1 – Quadrilaterals

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