NCERT Class 9 Maths Chapter 8 Quadrilaterals Solutions
NCERT Class 9 Maths Chapter 8 Quadrilaterals Solutions Exercise 8.1 Q.1. The angles of a quadrilateral are the ratio 3:5: 9:13. Find all the angles of the quadrilateral. Ans: Let ABCD be a quadrilateral in which ∠A: ∠B:∠C:∠D=3:5:9:13 Sum of the ratios = 3 + 5 + 9 + 13 = 30 Also, ∠ A+∠B+∠C+ ∠ D = 360⁰ | Sum of all the angles of a quadrilateral is 360⁰ Q.2. If the diagonals of a parallelogram are equal, then show that it is a rectangle. Ans: Given: In parallelogram ABCD, AC = BD To Prove: || gm ABCD is a rectangle. Proof: In ∆ ACB and ∆ BDA AC = BD | Given AB = BA | Common BC = AD | Opposite sides of || gm ABCD ∴ ACB ≅ ∆BDA | ISSS Rule ∴ ∠ ABC = ∠ BAD …(1) c.p.c.t. Again,∵ AD || BC | Opp. sides of || gm ABCD and transversal AB intersects them ∴ ∠BAD+∠ABC = 180⁰…(2) Sum of consecutive interior angles on the same side of the transversal is 180⁰ From (1) and (2), ∠BAD=∠ABC = 90⁰ ∴ ∠ A = 90⁰ ∴ || gm ABCD is a rectangle. Q.3. Show that if the dia...