In Δ PQR, D is the mid-point of QR. 

PM is _______________

PD is ________________

Is QM = MR?

Draw rough sketches for the following:

1. In Δ ABC, BE is a median.

2. In Δ PQR, PQ and PR are altitudes of the triangle.

3. In Δ XYZ, 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.

Find the value of the unknown exterior angle x in the following diagrams:

Find the value of the unknown interior angle x in the following figures:

Find the value of unknown x in the following diagrams:

Find the values of the unknowns x and y in the following diagrams:

Is it possible to have a triangle with the following sides?

1. 2 cm, 3 cm, 5 cm

2. 3 cm, 6 cm, 7 cm

3. 6 cm, 3 cm, 2 cm

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

1. OP + OQ > PQ?                        

2. OQ + OR > QR?                  

3. OR + OP > RP?

AM is a median of a triangle ABC. Is AB + BC + CA > 2AM? (Consider the sides of triangles Δ ABM and Δ AMC.)

ABCD is a 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?

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?

1. 2.5 cm, 6.5 cm, 6 cm

2. 2 cm, 2 cm, 5 cm

3. 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 Δ PQR are 25⁰ and 65⁰.

Write which of the following is true: 

1. PQ² + QR² = RP²

2. PQ² + RP² = QR²

3. RP² + QR² = PQ²

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.