Ncert solutions mathematics class 7 Solutions for Chapter 6 the triangle and its properties

Exercises in Chapter 6 the triangle and its properties Grade 7

Exercise 6.1

Exercise 6.2

Exercise 6.3

Exercise 6.4

Exercise 6.5

Questions in Exercise 6.1

In Δ PQR, D is the mid-point of $\overline{QR}$ .

$\overline{PM}$ is_.

Q1) In ∆ PQR, D is the mid-point of QR .

PM is _____________.

PD is _____________.

Is QM = MR?

In Δ PQR, D is the mid-point of $\overline{QR}$ .

PD is _____________.

In Δ PQR, D is the mid-point of $\overline{QR}$ .

Is QM = MR?

Draw rough sketches for the following:

In ΔABC, BE is a median.

Draw rough sketches for the following:

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

Draw rough sketches for the following:

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

Q2) Draw rough sketches for the following:

(a) In ∆ABC, BE is a median.

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

Q3) Verify by drawing a diagram if the median and altitude of an isosceles triangle can be same.

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

Questions in Exercise 6.2

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

Q1) Find the value of the unknown exterior angle x in the following diagrams:

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

Q2) Find the value of the unknown interior angle x in the following figures:

(i}

(ii)

(iii)

(iv)

(v)

(vi)

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

Questions in Exercise 6.3

Q1) Find the value of the unknown x in the following diagrams:

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

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

Q2) Find the values of the unknowns x and y in the following diagrams:

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

6 cm, 3 cm, 2 cm

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

Questions in Exercise 6.4

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

3 cm, 6 cm, 7 cm

Q1) 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

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

2 cm, 3 cm, 5 cm

Q2) Take any point O in the interior of a triangle PQR. Is

(i) OP + OQ > PQ?

(ii) OQ + OR > QR?

(iii) OR + OP > RP?

Take any point O in the interior of a triangle PQR. Is OP + OQ > PQ?

Take any point O in the interior of a triangle PQR. Is OR + OP > RP?

Take any point O in the interior of a triangle PQR. Is OQ + OR > QR?

AM is a median of a triangle ABC.

Is AB + BC + CA > 2 AM?

(Consider the sides of triangles ΔABM and ΔAMC.)

Q3) AM is a median of a triangle ABC. Is AB + BC + CA > 2 AM?

(Consider the sides of triangles ∆ABM and ∆AMC.)

Q4) ABCD is a quadrilateral. Is AB + BC + CD + DA > AC + BD?

ABCD is a quadrilateral.

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

Q5) ABCD is quadrilateral. Is AB + BC + CD + DA < 2 (AC + BD)?

ABCD is quadrilateral. Is AB + BC + CD + DA < 2 (AC + BD)

Q6) 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?

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?

Questions in Exercise 6.5

Q1) PQR is a triangle, right-angled at P. If PQ = 10 cm and PR = 24 cm, find QR.

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

Q2) ABC is a triangle, right-angled at C. If AB = 25 cm and AC = 7 cm, find BC.

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

Q3) 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.

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?

2 cm, 2 cm, 5 cm.

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

2.5 cm, 6.5 cm, 6 cm.

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

1.5 cm, 2cm, 2.5 cm.

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

Q4) 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, 2cm, 2.5 cm.

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.

Q5) 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:

PQ2 + RP2 = QR2