Someone please solve these:
+=4 and −=2
1. To verify the conditions for consistency of a system of linear equations in two variables by graphical method
2. To verify that the given sequence is an arithmetic progression by paper cutting and pasting method
3. To verify that the sum of first n-natural numbers is (+) by graphical method
4. To verify Basic Proportionality theorem using parallel line board and triangle cut-outs
5. To verify the Pythagoras Theorems by the method of paper folding , cutting and pasting
6. To verify “ The ratio of the areas of two similar triangles is equal to the ratio of the square of their corresponding sides” by performing an activity.
7. To verify using the method of paper cutting, pasting and folding that the lengths of tangents drawn from an external point are equal
8. To obtain the formula for area of the circle by coiling method.
9. To make a clinometers and use it to measure the height of an object
10. To compare the volumes of two right circular cylinders which are formed from two rectangles sheets with same dimension
11. To get familiar with the idea of probability of an event through a double colour card experiment
Answers
Answer:
To verify by a graphical method that the sum of the first ti natural numbers is
Materials Required
A sheet of white paper
A geometry box
A tube of glue
A long, colored paper tape of uniform width (say, 1 unit)
A pencil
Theory
The sum of the first n terms of an AP is given by
Taking a = 1 and d = 1, the AP becomes 1,2, 3, 4, …
∴ putting a =1 and d = 1 in equation (i), we get
i.e., the sum of the first n natural numbers =
Procedure
Step 1: We shall verify the formula for the first 10 natural numbers, i.e., for n = 10.
Step 2: Draw horizontal and vertical lines on the sheet of white paper to mark squares, each of size 1 unit x 1 unit.
Step 3: Cut the colored paper tape in 10 rectangular strips of lengths 1 unit, 2 units, 3 units, …, 10 units.
Step 4: Paste these strips on the grid sequentially as shown in Figure 4.1.
Step 5: Complete the rectangle ABCD so that AB = 11 units and BC = 10 units.
Step 6: Cut the portion of the rectangle ABCD which is covered by the colored paper strips. We find that this portion completely covers the remaining portion of the rectangle ABCD.