Скачать или смотреть LATEST NCERT CLASS 7 MATHS( GANITA PRAKASH )CHAPTER 7F A TALE OF INTERSECTING LINES 156,157,158, 159

LATEST NCERT CLASS 7 MATHS ( GANITA PRAKASH ) CHAPTER 7F A TALE OF INTERSECTING LINES PAGES 156, 157, 158, 159

FIGURE IT OUT

1. Which of the following lengths can be the sidelengths of a triangle?
Explain your answers. Note that for each set, the three lengths have
the same unit of measure.
(a) 2, 2, 5
(b) 3, 4, 6
(c) 2, 4, 8
(d) 5, 5, 8
(e) 10, 20, 25
(f) 10, 20, 35
(g) 24, 26, 28

Will triangles always exist when a set of lengths satisfies the triangle
inequality? How can we be sure?

We can be sure of the existence of a triangle only if we can show that
the circles intersect internally (as in Fig. 7.5) whenever the triangle inequality is satisfied. But are there other possibilities when the two circles are constructed? Let us visualise and study them.

Note that while constructing the circles, we take
(a) the length of the base AB = longest of the given length
(b) the radii of the circles to be the smaller two lengths.

Which of the above-mentioned cases will lead to the formation of a triangle? Clearly, triangles are formed only when the circles intersect each other internally (Case 3).

Let us study each of these cases by finding the relation between the radii (the smaller two lengths) and AB (longest length).

CASE 1 - CIRCLES TOUCH EACH OTHER AT A POINT

sum of the two radii = AB
or
sum of the two smaller lengths = longest length

CASE 2 - CIRCLES DONOT INTERSECT INTERNALLY
For this case to happen, what should be the relation between the radii
and AB?
It can be seen from the figure that,
sum of the two radii less than AB
or
sum of the the two smaller lengths less than longest length

CASE 3 - CIRCLES INTERSECT EACH OTHER
AB is composed of one radius and a part of the other. So, sum of the two radii greater than AB,
or
sum of the two smaller lengths greater than longest length

Can we use this analysis to tell if a triangle exists when the lengths
satisfy the triangle inequality?

How will the two circles turn out for a set of lengths that do not satisfy
the triangle inequality? Find 3 examples of sets of lengths for which the circles:
(a) touch each other at a point,
(b) do not intersect.

Frame a complete procedure that can be used to check the existence of
a triangle.