6. Angles Q and R of a are and . Write which of the following is true:
4. Which of the following can be the sides of a right triangle?
(i) , , 6 cm.
(ii) 2 cm, 2 cm, 5 cm.
(iii) , 2cm, .
In the case of right-angled triangles, identify the right angles.
3. A 15 m long ladder reached a window 12 m high from the ground on placing it against a wall at a distance a. Find the distance of the foot of the ladder from the wall.
Here. As we can see, The ladder with wall forms a right-angled triangle with
the vertical height of the wall = perpendicular = 12 m
length of ladder = Hypotenuse = 15 m
Now, As we know
In a Right-angled Triangle: By Pythagoras Theorem,
Hence the distance of the foot of the ladder from the wall is 9 m.
2. ABC is a triangle, right-angled at C. If and , find BC.
1. PQR is a triangle, right-angled at P. If and , find QR.
Q. Find the unknown length x in the following figures (Fig ):
5. ABCD is quadrilateral. Is
4. ABCD is a quadrilateral.
6. The lengths of two sides of a triangle are 12 cm and 15 cm. Between what two measures should the length of the third side fall?
3. AM is a median of a triangle ABC.
(Consider the sides of triangles and .)
2. Take any point O in the interior of a triangle PQR. Is
1. Is it possible to have a triangle with the following sides?
(i) 2 cm, 3 cm, 5 cm (ii) 3 cm, 6 cm, 7 cm
(iii) 6 cm, 3 cm, 2 cm
2. Find angles x and y in each figure.
1. Find angle x in each figure:
2. Find the values of the unknowns x and y in the following diagrams
1. Find the value of the unknown x in the following diagrams
2. Find the value of the unknown interior angle in the following figures:
1. Find the value of the unknown exterior angle x in the following diagrams:
3. Is something wrong in this diagram (Fig )? Comment.
1. Exterior angles can be formed for a triangle in many ways. Three of them are shown here (Fig )
There are three more ways of getting exterior angles. Try to produce those rough sketches.