#### Chapters

Chapter 2: Fractions and Decimals

Chapter 3: Data Handling

Chapter 4: Simple Equations

Chapter 5: Lines and Angles

Chapter 6: The Triangle and its Properties

Chapter 7: Congruence of Triangles

Chapter 8: Comparing Quantities

Chapter 9: Rational Numbers

Chapter 10: Practical Geometry

Chapter 11: Perimeter and Area

Chapter 12: Algebraic Expressions

Chapter 13: Exponents and Powers

Chapter 14: Symmetry

Chapter 15: Visualising Solid Shapes

#### NCERT Mathematics Class 7

## Chapter 6: The Triangle and its Properties

#### Chapter 6: The Triangle and its Properties Exercise 6.10 solutions [Page 116]

In ΔPQR, D is the mid-point of `bar(QR)`

`bar(PM)` is _________

PD is __________

Is QM = MR?

Draw rough sketches for the following

In ΔABC, BE is a median.

Draw rough sketches for the following:

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

Draw rough sketche for the following:

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.

#### Chapter 6: The Triangle and its Properties Exercise 6.20 solutions [Pages 118 - 119]

Find the value of the unknown exterior angle *x* in the Given diagrams:

Find the value of the unknown exterior angle *x* in the Given diagrams:

Find the value of the unknown exterior angle *x* in the Given diagrams:

Find the value of the unknown exterior angle *x* in the Given diagrams:

Find the value of the unknown exterior angle *x* in the Given diagrams:

Find the value of the unknown exterior angle *x* in the Given diagrams:

Find the value of the unknown interior angle *x* in the following figure.

Find the value of the unknown interior angle *x* in the following figure.

Find the value of the unknown interior angle *x* in the following figure.

Find the value of the unknown interior angle *x* in the following figure.

Find the value of the unknown interior angle *x* in the following figure.

Find the value of the unknown interior angle *x* in the following figure.

#### Chapter 6: The Triangle and its Properties Exercise 6.30 solutions [Page 121]

Find the value of the unknown *x* in the given diagram:

Find the value of the unknown *x* in the given diagram:

Find the value of the unknown *x* in the given diagram:

Find the value of the unknown *x* in the given diagram:

Find the value of the unknown *x* in the given diagram:

Find the value of the unknown *x* in the given diagram:

Find the value of the unknowns *x* and *y* in the following diagrams:

Find the value of the unknowns *x* and *y* in the following diagrams:

Find the value of the unknowns *x* and *y* in the following diagram:

Find the value of the unknowns *x* and *y* in the following diagram:

Find the value of the unknowns *x* and *y* in the following diagram:

Find the value of the unknowns *x* and *y* in the following diagram:

#### Chapter 6: The Triangle and its Properties Exercise 6.40 solutions [Pages 126 - 127]

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

2 cm, 3 cm, 5 cm

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

3 cm, 6 cm, 7 cm

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

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 > 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?

#### Chapter 6: The Triangle and its Properties Exercise 6.50 solutions [Page 130]

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?

2.5 cm, 6.5 cm, 6 cm

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

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

2 cm, 2 cm, 5 cm

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

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

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:

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

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

(3) 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.

## Chapter 6: The Triangle and its Properties

#### NCERT Mathematics Class 7

#### Textbook solutions for Class 7

## NCERT solutions for Class 7 Mathematics chapter 6 - The Triangle and its Properties

NCERT solutions for Class 7 Maths chapter 6 (The Triangle and its Properties) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the CBSE Mathematics for Class 7 solutions in a manner that help students grasp basic concepts better and faster.

Further, we at Shaalaa.com are providing such solutions so that students can prepare for written exams. NCERT textbook solutions can be a core help for self-study and acts as a perfect self-help guidance for students.

Concepts covered in Class 7 Mathematics chapter 6 The Triangle and its Properties are Introduction of Triangle, Medians of a Triangle, Altitudes of a Triangle, Exterior Angle of a Triangle and Its Property, Angle Sum Property of a Triangle, Two Special Triangles : Equilateral and Isosceles, Sum of the Lengths of Two Sides of a Triangle, Right-angled Triangles and Pythagoras Property.

Using NCERT Class 7 solutions The Triangle and its Properties exercise by students are an easy way to prepare for the exams, as they involve solutions arranged chapter-wise also page wise. The questions involved in NCERT Solutions are important questions that can be asked in the final exam. Maximum students of CBSE Class 7 prefer NCERT Textbook Solutions to score more in exam.

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