AUTUMN BREAK HOMEWORK CLASS- IX(MATHEMATICS)

 KENDRIYA VIDYALAYA NO-2, DARBHANGA

AUTUMN BREAK HOMEWORK

CLASS- IX(MATHEMATICS) 1. Three angles of a quadrilateral are equal and the fourth angle is equal to 144°. Find each of the equal angles of the quadrilateral. 2. If one angle of a parallelogram is 30° less than twice the smallest angle, then find the measure of each angle.

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4. ABCD is a parallelogram and AP and CQ are perpendiculars from vertices A and C on diagonal BD (see fig.). Show that : (i) AAPB ≅ ACQD (ii) AP = CQ

5. Show that the diagonals of a sqaure are equal and bisect each other at right angles.

6. ABCD is a rhombus. Show that diagonal AC bisects angle A as well as angle C and diagonal BD bisects angle B as well as angle D.

7. State and prove MID-POINT theorem.

8. Show that the line segments joining the mid-points of the opposite sides of a quadrilateral bisect each other.

9. Prove that the angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle.

10. Prove that equal chords of a circle are equidistant from the centre.