(b) In ΔPQR, PQ and PR are altitudes of the triangle.

(c) In ΔXYZ, YL is an altitude in the exterior of the triangle.

Verify by drawing a diagram if the median and altitude of an isosceles triangle can be same.

EXERCISE-6.2

Find the value of the unknown exterior angle xin the following diagrams:

Find the value of the unknown interior angle xin the following figures:

EXERCISE-6.3

Find the value of the unknown xin the following diagrams:

Find the value of the unknowns xand y in the following diagrams:

EXERCISE-6.4

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

Take any point O in the interior of a triangle PQR. Is

(i) OP + OQ > PQ?

(ii) OQ + OR > QR?

(iii) OR + OP > RP?

AM is a median of a triangle ABC.

Is AB + BC + CA > 2 AM?

(Consider the sides of triangles ΔABM and ΔAMC.)

ABCD is quadrilateral.

Is AB + BC + CD + DA >AC + BD?

ABCD is quadrilateral.

Is AB + BC + CD + DA < 2
(AC + BD)?

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?

EXERCISE-6.5

PQR is a triangle right angled at P. If PQ = 10 cm and PR = 24 cm, find QR.

ABC is a triangle right angled at C. If AB = 25 cm and AC = 7 cm, find BC.

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.

Which of the following can be the sides of a right triangle?

(i) 2.5 cm, 6.5 cm, 6 cm

(ii) 2 cm, 2 cm, 5 cm

(iii) 1.5 cm, 2 cm, 2.5 cm

In the case of right-angled triangles, identify the right angles.

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.

Angles Q and R of a ΔPQR are 25° and 65°.

Write which of the following is true:

(i) PQ^{2} + QR^{2}= RP^{2}

(ii) PQ^{2} + RP^{2}= QR^{2}

(iii) RP^{2} + QR^{2}= PQ^{2 }

Find the perimeter of the rectangle whose length is 40 cm and a diagonal is 41 cm.

The diagonals of a rhombus measure 16 cm and 30 cm. Find its perimeter.