Question

1 Adjacent angles of a parallelogram are ----------------

2 The diagonals of a square or rhombus are ---------------

3 The diagonals of a parallelogram --------------- each other.

4 In a parallelogram, opposite angles are ---------------

5 ABCD is a rhombus. If P,Q,R,S are the mid points of

AB, BC, CD, DA respectively, then PQRS is a -----------------

6 If a pair of opposite sides of a quadrilateral is equal and parallel, then

the quadrilateral is a -----------------------

7 Given a ΔABC, parallel lines are drawn through A, B and C

respectively to sides BC, CA and AB forming ΔPQR.

Prove that BC = 1

2

QR

8 D, E and F are the mid points of sides AB, BC and CA respectively

of an isosceles ΔABC. Prove that ΔEDF is also isosceles.

9 Prove that the quadrilateral formed by the internal angle bisectors of

any quadrilateral is cyclic.

10 Prove that the sum of angles of a quadrilateral is 3600​

Answer 1

Answer:

The angles of quadrilateral are in the ratio 3 : 5 : 9 : quadrilateral.

Sol: Let the angles of the quadrilateral be 3x, 5x, 9x and 13x.

∵ Sum of all the angles of quadrilateral = 360°

∴ 3x + 5x + 9x + 13x = 360°

⇒ 30x = 360°

∴ 3x = 3 × 12° = 36°

5x = 5 × 12°= 60°

9x = 9 × 12° = 108°

13x = 13 × 12° = 156°

⇒ The required angles of the