Chapter 9 – Areas of Parallelogram and Triangles

8. If the medians of a ∆ ABC intersect at G, show that ar (AGB) = ar (AGC) = ar (BGC) = 1/3 ar (ABC) 8. If the medians of a ∆ ABC intersect at G show that ar (AGB) = ar (AGC) = ar (BGC) = 1/3 ar (ABC) July 1, 2021 Category: Chapter [...]

7. In Fig. 9.25, ABCDE is any pentagon. BP drawn parallel to AC meets DC produced at P and EQ drawn parallel to AD meets CD produced at Q. Prove that ar (ABCDE) = ar (APQ) 7. In Fig. 9.25 ABCDE is any pentagon. BP drawn parallel to AC meets DC produced at P and [...]

6. In ∆ ABC, if L and M are the points on AB and AC, respectively such that LM || BC. Prove that ar (LOB) = ar (MOC) 6. In ∆ ABC if L and M are the points on AB and AC respectively such that LM || BC. Prove that ar (LOB) = ar [...]

5. ABCD is a trapezium in which AB || DC, DC = 30 cm and AB = 50 cm. If X and Y are, respectively the mid-points of AD and BC, prove that ar (DCYX) = 7/9 ar (XYBA) 5. ABCD is a trapezium in which AB || DC DC = 30 cm and AB [...]

4. In Fig. 9.24, CD || AE and CY || BA. Prove that ar (CBX) = ar (AXY) 4. In Fig. 9.24 CD || AE and CY || BA. Prove that ar (CBX) = ar (AXY) July 1, 2021 Category: Chapter 9 - Areas of Parallelogram and Triangles , Maths , NCERT Class 9 ,

3. The medians BE and CF of a triangle ABC intersect at G. Prove that the area of ∆ GBC = area of the quadrilateral AFGE. 3. The medians BE and CF of a triangle ABC intersect at G. Prove that the area of ∆ GBC = area of the quadrilateral AFGE. July 1, 2021 [...]

2. The diagonals of a parallelogram ABCD intersect at a point O. Through O, a line is drawn to intersect AD at P and BC at Q. Show that PQ divides the parallelogram into two parts of equal area. 2. The diagonals of a parallelogram ABCD intersect at a point O. Through O a line [...]

1. A point E is taken on the side BC of a parallelogram ABCD. AE and DC are produced to meet at F. Prove that ar (ADF) = ar (ABFC) 1. A point E is taken on the side BC of a parallelogram ABCD. AE and DC are produced to meet at F. Prove that [...]

9. If the mid-points of the sides of a quadrilateral are joined in order, prove that the area of the parallelogram so formed will be half of the area of the given quadrilateral (Fig. 9.19). [Hint: Join BD and draw perpendicular from A on BD.] 9. If the mid-points of the sides of a quadrilateral [...]

8. In trapezium ABCD, AB || DC and L is the mid-point of BC. Through L, a line PQ || AD has been drawn which meets AB in P and DC produced in Q (Fig. 9.18). Prove that ar (ABCD) = ar (APQD) 8. In trapezium ABCD a line PQ || AD has been drawn [...]