Take a cut-out a parallelogram, say, ABCD (see figure). Let its diagonals bar(AC) and bar(DB) meet at O. Find the mid-point of bar(AC) by a fold, placing C on A. Is the mid-point same as O? Does this show that diagonal bar(DB) bisects the diagonal bar(AC) at the point O ? Discuss it with your friends. Repeat the activity to find where the mid-point of bar(DB) could lie.

Take a thick white sheet. Fold the paper once. Draw two line segments of different lengths as shown in the figure. Cut along the line segments and open up. You have the shape of a kite. Has the kite any line symmetry ? Fold both the diagonals of the kite. Use the set-square to check if they cut at right angles. Are the diagonals equal in length ? Verify (by paper-folding or measurement) if the diagonals bisect each other. By folding an angle of the kite. on its opposite check for angles of equal measure. Observe the diagonal folds, do they indicate any diagonal being an angle bisector ? Share your findings with others and list them. A summary of these results are given elsewhere in the chapter for your reference.

The Class X students of a secondary school in Krishinagar have been allotted a rectangular plot of land for their gardening activity. Sapling of Gulmohar are planted on the boundary at a distance of lm from each other. There is a triangular grassy lawn in the plot as shown in the Fig. The students are to sow seeds of flowering plants on the remaining area of the plot.:- Taking A as origin find the coordinates of the vertices of triangle .What will be the coordinates of the vertices of triangle PQR if C is the origin ? Also calculate the areas of the triangles in these cases. What do you observe ?

The vertices of a triangle are (1, a), (2, b) and (c^2, -3). (i) Prove that its centroid can not lie on the y-axis. (ii) Find the condition that the centroid may lie on the x-axis for any value of a, b, c in RR.

We know that 3+5=5+3=8 that is the whole numbers can be added in any order . In other words , addition is commutative for whole numbers Can we say the same fot integers also ? We have 5+(-6)=(-6)+5 Are the following equal ? (i) (-8)+(-9)and(-9)+(-8) (ii) (-23)+32and32+(-23) (iii) (-45)+0and0+(-45) Try this with five other pairs of inegers .Do you find any pairs of intergers for which the sums are different when the order is changed ?

Given below is a square of letters in which are hidden different words related to respiration in organisms. These words may be present in any direction - upwards, downwards or along the diagonals. Find the words for your respiratory system. Clues about those words are given below the square. (i) The air tubes of insects (ii) Skeletal structures surrounding chest cavity (iii) Muscular floor of chest cavity (iv) Tiny pores on the surface of leaf (v) Small openings on the sides of the body of an insect. (vi) The respiratory organs of human beings (vii) The openings through which we inhale (viii) An anaerobic organism An organism with tracheal system .

Take identical cut outs of congruent triangles of sides 3 cm ,4cm , 5cm Arrange them as shown . You get a trapezium (check if) which are the parallel sides here ? should the non -parallel sides be equal ? You can get two more trapeziums using the same set of triangles. Find them out and discuss their shapes.

If the pair of tangents are drawn from the point (4,5) to the circle x^(2)+y^(2)-4x-2y-11=0 , then (i) Find the length of chord of contact. (ii) Find the area of the triangle fromed by a pair of tangents and their chord of contact. (iii) Find the angle between the pair of tangents.

When two triangles, say ABC and PQR are given, there are, in all, six possible matchings or correspondences. Two of them are (i) ABC PQR and (ii) ABC QRP. Find the other four correspondences by using two cutouts of triangles. Will all these correspondences lead to congruence? Think about it.