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Practice Time 8C

1. Which of the followings can be the sides of a right-angled triangle?

(a) 2.5 cm, 6 cm, 6.5 cm (b) 6 cm, 7 cm, 9 cm
(c) 12 cm, 5 cm, 13 cm (d) 3 cm, 4 cm, 5 cm
2. Find the unknown length x in the following figures.

(a) A (b) A (c) A (d) 24

8 cm x cm x m 26 m x m 24 m 25 m x 7
B D C
B 6 cm C B 24 m C 17 m

(e) (f) x
37 37
12 3
x 12 cm 5 cm
3. ABC is a triangle, right-angled at C. If AB = 25 cm and AC = 7 cm, find BC.
4. Find the length of the diagonal of a rectangle whose length is 24 cm and breadth is 7 cm.
5. The perimeter of a rectangular plot is 56 m. If the length of the plot is 16 m, find the length of its
diagonal.
6. A 26 m long ladder leans against a wall. If the top of the ladder touches the wall 24 m above the
ground, find the distance between the foot of the ladder and foot of the wall.
7. A tree is broken at a height of 5 m from the ground and its top touches the ground at a distance of
12 m from the base of the tree. Find the original height of the tree.
8. Robin drives 41 km towards North and then 9 km to the East. Find the distance between the starting
and terminating point.
9. Somya walks 6 km due East and then 8 km due North. How far is she from her starting place?

Introduction to Congruence

We will now study a new geometrical concept.

Before we begin this new concept, look at the different pairs of pictures given below and answer
the questions asked about every picture.

If one picture is placed over the second picture, will the first picture overlap the second picture
exactly and completely?
The answer to this questions for each of the pictures given above is ‘yes’.

Such objects which are exactly the same shape and size are called congruent objects.
The symbol of congruency is “≅”. If we wish to state that P is congruent to P , we write P ≅ P .
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185 The Triangle and Its Properties