Class 9 – Polynomials

Example 8: l, m and n are three parallel lines intersected by transversals p and q such that l, m and n cut off equal intercepts AB and BC on p (see Fig. 8.28). Show that l, m and n…

Example 7: In ∆ ABC, D, E and F are respectively the mid-points of sides AB, BC and CA (see Fig. 8.27). Show that ∆ ABC is divided into four congruent triangles by joining D, E and F. Example 6…

Example 6: 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: (i) APCQ is a…

Example 5: Show that the bisectors of angles of a parallelogram form a rectangle. Example 4 Example 6

Example 4: Two parallel lines l and m are intersected by a transversal p (see Fig. 8.15). Show that the quadrilateral formed by the bisectors of interior angles is a rectangle. Example 3 Example 5

Example 3: ABC is an isosceles triangle in which AB = AC. AD bisects exterior angle PAC and CD || AB (see Fig. 8.14). Show that (i) ∠ DAC = ∠ BCA and (ii) ABCD is a parallelogram Example 2…

Example 2: Show that the diagonals of a rhombus are perpendicular to each other.  IMP:- The proof is same for square and rhombus.  Example 1 Example 3