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# Maths IX A, B, C, D

Q1. Show that each angle of a rectangle is a right angle.

Q2. Show that the diagonals of a rhombus are perpendicular to each other.

Q3. Two parallel lines l and m are intersected by transversal p .show that quadrilateral formed by the bisectors of interior angles is a rectangle.

Q4.Show that the bisectors of angles of a parallelogram from a rectangle.

Q5. ABCD is a parallelogram in which p and q are mid-points of opposite sides AB and CD. If AQ intersects DP at S and BQ intersects CP at R, show that:

1. APCQ is a parallelogram.

2. DPBQ is a parallelogram.

3. PSQR is a parallelogram.

Q6. In triangle ABC,D,E and F are respectively the mid-points of sides AB,BC and CA. show that triangle ABC is divided into four congruent triangles by joining D, E and F.

Q7. L,m and n are three parallel lines intersected by transversals p such that l,m and n cut off equal intercepts AB and BC on p. show that l,m, and n cut off equal intercepts DE and EF on q also.

Q8. ABCD is a parallelogram and EFCD is a rectangle. Also AL perpendicular DC. Prove that.

1. Ar (ABCD) = ar (EFCD)

2. Ar (ABCD)= ar DCxAL

Q9. If a triangle and parallelogram are on the same base and between the same parallel,then prove that the area of the triangle is equal to half the area of the parallelogram.

Q10. Show that a median of a triangle divided it into two triangle of equal area.

Q11. ABCD is a quadrilateral and BE parallel AC and also BE meet DC produced at E.show that area of triangle ADE is equal to the area of the quadrilateral ABCD.

Q12. If two intersecting chords of a circle make equal with the diameter pass

Date of submission: 2 Jan 2015