Chapter 11 Circles Ex 11.2 eng
Chapter 11 Circles Ex 11.2 Question 1. Recall that two circles are congruent, if they have the same radii. Prove that equal chords of congruent circles subtend equal angles at their centres Solution: Given MN and PQ are two equal chords of two congruent circles with centre at O and O’. To prove ∠ MON […]
Chapter 11 Circles Ex 11.1 eng
Chapter 11 Circles Ex 11.1 Question 1. Fill in the blanks. (i) The centre of a circle lies in ___ of the circle. (exterior/interior) (ii) A point, whose distance from the centre of a circle is greater than its radius lies in ____ of the circle, (exterior/interior) (iii) The longest chord of a circle is […]
Chapter 10 Areas of Parallelograms and Triangles Ex 10.4 eng
Chapter 10 Areas of Parallelograms and Triangles Ex 10.4 Question 1. Parallelogram ABCD and rectangle ABEF are on the same base AB and have equal areas. Show that the perimeter of the parallelogram is greater than that of the rectangle. Solution: Given: parallelogram ABCD and rectangle ABEF are on same base AB, and area of both […]
Chapter 10 Areas of Parallelograms and Triangles Ex 10.3 eng
Chapter 10 Areas of Parallelograms and Triangles Ex 10.3 Question 1. In figure, E is any point on median AD of a ∆ABC. Show that ar (ABE) = ar (ACE). Solution: Given: AD is a median of AABC and E is a any point on AD. ∵ AD is the median of ∆ABC. ar (∆ABD) = […]
Chapter 10 Areas of Parallelograms and Triangles Ex 10.2 eng
Chapter 10 Areas of Parallelograms and Triangles Ex 10.2 Question 1. In figure, ABCD is a parallelogram, AE ⊥ DC and CF ⊥ AD. If AB = 16 cm, AE = 8 cm and CF = 10 cm, find AD. Solution: We know that, Area of parallelogram = Base x Altitude Given, AE = 8 […]
Chapter 10 Areas of Parallelograms and Triangles Ex 10.1 eng
Chapter 10 Areas of Parallelograms and Triangles Ex 10.1 Question 1. Which of the following figures lie on the same base and between the same parallels. In such a case, write the common base and the two parallels. Solution: In Fig. (i), APDC and trape∠ium ABCD Wes on the same base DC and between the […]
Chapter 9 Quadrilaterals Ex 9.2 eng
Chapter 9 Quadrilaterals Ex 9.2 Question 1. ABCD is a quadrilateral in which P, Q, R and S are mid-points of the sides AB, BC, CD and DA (see figure). AC is a diagonal. Show that (ii) PQ = SR (iii) PQRS is a parallelogram. Solution: (iii) Now, from Eqs. (i) and (iii), we get PQ […]
Chapter 9 Quadrilaterals Ex 9.1 eng
Chapter 9 Quadrilaterals Ex 9.1 Question 1. The angles of quadrilateral are in the ratio 3 : 5 : 9 : 13. Find all the angles of the quadrilateral. Solution: Question 2. If the diagonals of a parallelogram are equal, then show that it is a rectangle. Solution: Let given parallelogram is ABCD whose diagonals […]
Chapter 8 Linear Equations in Two Variables Ex 8.4 eng
Chapter 8 Linear Equations in Two Variables Ex 8.4 Question 1. Give the geometric representations of y = 3 as an equation (i) in one variable. (ii) in two variables. Solution: The given linear equation is y=3 …(i) (i) The representation of the solution on the number line is shown in the figure below, where y […]
Chapter 8 Linear Equations in Two Variables Ex 8.3 eng
Chapter 8 Linear Equations in Two Variables Ex 8.3 Question 1. Draw the graph of each of the following linear equations in two variables (i) x + y = 4 (ii) x – y = 2 (iii) y = 3x (iv) 3 = 2x + y Solution: (i) x + y = 4 To draw […]